
<PAGE>

                                 EXHIBIT 7.(g)
                                 -------------

                              FOUR MEDIA COMPANY
                            A Delaware Corporation
                         ----------------------------

                                    BYLAWS



                                   ARTICLE I
                                 STOCKHOLDERS

     Section 1.1    Annual Meeting.  An annual meeting of stockholders for the
                    --------------
purpose of electing those directors whose terms of office expires at such
meeting and of transacting such other business as may properly come before it
shall be held each year at such date, time and place, either within or without
the State of Delaware, as may be specified by the Board of Directors.

     Section 1.2    Special Meetings.  Special meetings of stockholders shall be
                    ----------------
called by the Secretary as and when provided for by the Certificate of
Incorporation, as amended from time to time, of the Corporation (the
"Certificate").  Special meetings of stockholders for any purpose or purposes
may be held at such time and place either within or without the State of
Delaware as may be stated in the notice.

     Section 1.3    Notice of Meetings.  Written notice of stockholders
                    ------------------
meetings, stating the place, date, and hour thereof, and, in the case of a
special meeting, the purpose or purposes for which the meeting is called, shall
be given by the Chairman of the Board, the President, any Vice President, the
Secretary or any other officer, to each stockholder entitled to vote thereat at
least 10 days but not more than 60 days before the date of the meeting, unless a
different period is prescribed by law or the Certificate.

     Section 1.4    Quorum.  Except as otherwise provided by law or in the
                    ------
Certificate or elsewhere in these Bylaws, the holders of a majority in total
voting power of the outstanding shares of capital stock of the Corporation
entitled to vote at a meeting of the stockholders, present in person or
represented by proxy, shall constitute a quorum for the transaction of business
at any annual or special meeting of the stockholders.  In the absence of a
quorum, the chairman of the meeting or the holders of a majority in total voting
power of the shares of capital stock entitled to vote thereat that are present
in person or represented by proxy shall have the power to adjourn the meeting
from time to time in the manner provided in Section 1.5 of these Bylaws until a
quorum shall attend.

     Section 1.5    Adjournment.  Any meeting of stockholders, annual or
                    -----------
special, may adjourn from time to time to reconvene at the same or some other
place, and notice need not be
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given of any such adjourned meeting if the time and place thereof are announced
at the meeting at which the adjournment is taken. At the adjourned meeting, the
Corporation may transact any business which might have been transacted at the
original meeting. If the adjournment is for more than 30 days, or if after the
adjournment a new record date is fixed for the adjourned meeting, a notice of
the adjourned meeting shall be given to each stockholder of record entitled to
vote at the meeting.

     Section 1.6    Voting.  Except as otherwise provided by law, the
                    ------
Certificate or elsewhere in these Bylaws and except for the election of
directors, at any meeting duly called and held at which a quorum is present, the
affirmative vote of a majority of the combined voting power of the shares
present in person or represented by proxy at the meeting and entitled to vote
upon a given question shall decide such question.  At any meeting duly called
and held for the election of directors of a particular class at which a quorum
is present, directors of such class shall be elected by a plurality of the
combined voting power of the shares present in person or represented by proxy at
the meeting and entitled to vote on the election of directors.

     Section 1.7    Organization.  The Chairman of the Board, or in his absence
                    ------------
the President, or in their absence any Vice President, shall call to order
meetings of stockholders and shall act as chairman of such meetings. The Board
of Directors or, if the Board of Directors fails to act, the stockholders may
appoint any stockholder, director, or officer of the Corporation to act as
chairman of any meeting in the absence of the Chairman of the Board, the
President and all Vice Presidents.  The Secretary of the Corporation shall act
as secretary of all meetings of stockholders, but, in the absence of the
Secretary, the chairman of the meeting may appoint any other person to act as
secretary of the meeting.

     Section 1.8    Order of Business.
                    -----------------

     (a)  Nominations of persons for election as directors of a particular class
of the Board of Directors of the Corporation and the proposal of business to be
considered by the stockholders may be made at any annual meeting of
stockholders, only (i) pursuant to the Corporation's notice of meeting, (ii) by
or at the direction of the Chairman of the Board or the Board of  Directors of
the Corporation or (iii) by any stockholder who is a holder of record at the
time of the giving of the notice provided for in this Section 1.8, who is
entitled to vote at the meeting and who complies with the procedures set forth
in this Section 1.8.

     (b)  For nominations or business properly to be brought before an annual
meeting by a stockholder, the stockholder must have given timely notice thereof
in proper written form to the Secretary of the Corporation.  To be timely, a
stockholder's notice must be delivered to the Secretary at the principal
executive offices of the Corporation not less than 70 days nor more than 120
days prior to the anniversary date of the immediately preceding annual meeting;
provided, however, that in the event that the date of the annual meeting is more
than 30 days earlier or more than 60 days later than such anniversary date,
notice by the stockholder to be timely must be so delivered not earlier than the
120th day prior to such annual meeting and not later than the close of business
on the later of the 70th day prior to such annual meeting or the 10th day
following the day on which public announcement of the date of such meeting is
first

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made. To be in proper written form, a stockholder's notice to the Secretary of
the Corporation shall set forth in writing as to each matter the stockholder
proposes to bring before the annual meeting: (i) as to each person whom the
stockholder proposes to nominate for election or re-election as a director or a
particular class, all information relating to such person that is required to be
disclosed in solicitations of proxies for election of directors in an election
contest, or is otherwise required pursuant to Regulation 14A under the
Securities Exchange Act of 1934, as amended (the "Exchange Act") and Rule 14a-11
thereunder (including such person's written consent to being named in the proxy
statement as a nominee and to serving as a director of such class if elected);
(ii) as to any other business that the stockholder proposes to bring before the
meeting, a brief description of the business desired to be brought before the
annual meeting, the reasons for conducting such business at the annual meeting,
any material interest in such business of such stockholder and the beneficial
owner, if any, on whose behalf the proposal is made, and in the event that such
business includes a proposal to amend the bylaws of the Corporation, the
language of the proposed amendment; and (iii) as to the stockholder giving the
notice and the beneficial owner, if any, on whose behalf the nomination or
proposal is made (a) the name and address of such stockholder, as they appear on
the Corporation's books, and of such beneficial owner; (b) the class or series
and number of shares of the Corporation which are owned beneficially and of
record by such stockholder and such beneficial owner and (c) a representation
that such stockholder is entitled to vote at such annual meeting and intends to
appear in person or by proxy at such meeting to nominate the person or propose
the business specified in the notice. The foregoing notice requirements shall be
deemed satisfied by a stockholder if the stockholder has notified the
Corporation of his or her intention to make a nomination or present a proposal
at an annual meeting and such stockholder's nominee or proposal has been
included in a proxy statement that has been prepared by management of the
Corporation to solicit proxies for such annual meeting.

     (c)  Only such business shall be conducted at a special meeting of
stockholders as shall have been brought before the meeting pursuant to the
Corporation's notice of meeting. Nominations of persons for election as
directors of a particular class of the Board of Directors of the Corporation may
be made at a special meeting of stockholders at which directors of such class
are to be elected pursuant to the  Corporation's notice of meeting (i) by or at
the direction of the Board of Directors or (ii) provided that the Board of
Directors has determined that directors of such class shall be elected at such
meeting, by any stockholder who is a holder of record at the time of the giving
of notice provided for in this Section 1.8, who is entitled to vote at the
meeting and who complies with the procedures set forth in Section 1.8.  In the
event the Corporation calls a special meeting of stockholders for the purpose of
electing one or more directors as a director or directors, as applicable, of a
particular class of the Board of Directors of the Corporation, any such
stockholder may nominate a person or persons (as the case may be) for election
to such position(s) as specified in the Corporation's notice of meeting, if the
stockholder has given timely notice thereof in proper written form to the
Secretary of the Corporation.  To be timely, a stockholder's notice must be
delivered to the Secretary at the principal executive offices of the Corporation
not earlier than the 120th day prior to such special meeting and not later than
the close of business on the later of the 70th day prior to such special meeting
or the 10th day following the day on which public announcement of the date of
such meeting is first made.  To

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be in proper written form, such notice must meet the requirements of either of
the last two sentences of paragraph (b) above.

     (d)  Only such persons who are nominated in accordance with the procedures
set forth in this Section 1.8 shall be eligible to serve as directors of the
Corporation and only such business shall be conducted at a meeting of
stockholders as shall have been brought before the meeting in accordance with
the procedures set forth in this Section 1.8.  Except as otherwise provided by
law, the Certificate or these Bylaws, the chairman of the meeting shall have the
power and duty to determine whether a nomination or any business proposed to be
brought before the meeting was made in accordance with the procedures set forth
in this Section 1.8 and, if any proposed nomination or business proposal is not
in compliance with this Section 1.8, to declare that such defective nomination
or business proposal shall be disregarded.

                                  ARTICLE II

                              BOARD OF DIRECTORS

     Section 2.1    Number and Term of Office.  The business, property, and
                    -------------------------
affairs of the Corporation shall be managed by or under the direction of a Board
of Directors of at least three directors.  The number and term of office of the
members of the Board of Directors shall be determined as set forth in the
Certificate.

     Section 2.2    Resignations.  Any director of the Corporation, or any
                    ------------
member of any committee, may resign at any time, by giving written notice to the
Board of Directors, the Chairman of the Board, the President or the Secretary of
the Corporation.  Any such resignation shall take effect after receipt of the
applicable written notice of resignation by the Board of Directors, the Chairman
of the Board, the President or the Secretary of the Corporation at the time
specified in such written notice or, if no time is specified, immediately upon
receipt of such written notice by the Board of Directors, the Chairman of the
Board, the President or the Secretary of the Corporation.  Unless otherwise
specified in such notice, the acceptance of such resignation shall not be
necessary to make it effective.

     Section 2.3    Removal of Directors.  Directors may only be removed as
                    --------------------
provided in Section C of Article V of the Certificate.

     Section 2.4    Newly Created Directorships and Vacancies.  Newly created
                    -----------------------------------------
directorships resulting from an increase in the number of directors and any
vacancy on the Board of Directors occurring for any other reason shall be filled
in accordance with Section D of Article V of the Certificate.

     Section 2.5    Chairman of the Board.  The directors shall elect one of
                    ---------------------
their members to be Chairman of the Board of Directors.  The Chairman shall
perform such duties as may from time to time be assigned to him by the Board of
Directors.  The Chairman shall be subject to the control of and may be removed
from such office by the Board of Directors.

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     Section 2.6    Annual Meetings. The annual meeting of the Board of
                    ---------------
Directors, for the election of officers and the transaction of such other
business as may come before the meeting, shall be held without notice at the
same place as, and immediately following, the annual meeting of the
stockholders.

     Section 2.7    Regular Meetings.  Regular meetings of the Board of
                    ----------------
Directors may be held without notice at such time and place as shall from time
to time be determined by the Board of Directors.

     Section 2.8    Special Meetings.  Special meetings of the Board of
                    ----------------
Directors shall be held at such time and place as shall be designated in the
notice of the meeting whenever called by the Chairman of the Board, the
President or by a majority of the directors then in office.  The Secretary, or
in his absence any other officer of the Corporation, shall give each director
notice of the time and place of holding of special meetings of the Board of
Directors by mail at least five days before the meeting, or by telegram, cable,
facsimile transmission or personal service at least 24 hours before the meeting.
Unless otherwise stated in the notice thereof, any and all business may be
transacted at any meeting without specification of such business in the notice.

     Section 2.9    Quorum.  A majority of the total number of members of the
                    ------
Board of Directors as constituted from time to time shall constitute a quorum
for the transaction of business.  If at any meeting of the Board of Directors
(whether or not adjourned from a previous meeting) there shall be less than a
quorum present, a majority of those present may adjourn the meeting to another
time and place, and the meeting may be held as adjourned without further notice
or waiver.

     Section 2.10  Manner of Acting.  Except as otherwise provided by law, the
                   ----------------
Certificate or these Bylaws, a majority of the directors present at any meeting
at which a quorum is present may decide any question brought before such
meeting.

     Section 2.11   Organization.  Meetings shall be presided over by the
                    ------------
Chairman of the Board, or in his absence by such other person as the directors
may select.  The Secretary of the Corporation shall act as secretary of the
meeting, but in his absence the chairman of the meeting may appoint any person
to act as secretary of the meeting.

     Section 2.12   Committees.  The Board of Directors may, by resolution
                    ----------
passed by not less than 75% of the members of the Board of Directors then in
office, designate one or more committees, each committee to consist of one or
more of the directors of the Corporation.  The Board of Directors may designate
one or more directors as alternate members of any committee, who may replace any
absent or disqualified member at any meeting of the committee.  In the absence
or disqualification of a member of a committee, the member or members thereof
present at any meeting and not disqualified from voting, whether or not he or
they constitute a quorum, may unanimously appoint another member of the Board of
Directors to act at the meeting in place of any such absent or disqualified
member.  Any such committee, to the extent provided in the resolution of the
Board of Directors, shall have and may exercise all the powers and authority of
the Board of Directors in the management of the business and affairs of the
Corporation, and may authorize the seal of the Corporation to be affixed to all
papers which may require it; but no

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such committee shall have power or authority in reference to the following
matters: (i) approving or adopting, or recommending to the stockholders, any
action or matter expressly required by the General Corporation Law of the State
of Delaware, as amended from time to time (the "DGCL"), to be submitted to
stockholders for approval or (ii) adopting, amending or repealing any Bylaw of
the Corporation. Each committee which may be established by the Board of
Directors pursuant to these Bylaws may fix its own rules and procedures. Notice
of meetings of committees, other than of regular meetings provided for by such
rules, shall be given to committee members. All action taken by committees shall
be recorded in minutes of the meetings.

     Section 2.13   Action Without Meeting.  Nothing contained in these Bylaws
                    ----------------------
shall be deemed to restrict the power of members of the Board of Directors, or
any committee designated by the Board of Directors, to take any action required
or permitted to be taken by them without a meeting.

     Section 2.14   Telephone Meetings.  Nothing contained in these Bylaws shall
                    ------------------
be deemed to restrict the power of members of the Board of Directors, or any
committee designated by the Board of Directors, to participate in a meeting of
the Board of Directors, or committee, by means of conference telephone or
similar communications equipment by means of which all persons participating in
the meeting can hear each other.  Participation in a meeting by any such means
shall constitute presence in person at such meeting.

                                  ARTICLE III

                                   OFFICERS

     Section 3.1    Executive Officers.  The executive officers of the
                    ------------------
Corporation shall be a Chairman of the Board, a President, one or more Vice
Presidents and a Secretary, each of whom shall be elected by the Board of
Directors.  The Board of Directors may elect or appoint such other officers
(including a Treasurer and one or more Assistant Secretaries) as it may deem
necessary or desirable.  Each officer shall hold office for such term as may be
prescribed by the Board of Directors from time to time.  Any person may hold at
one time two or more offices.

     Section 3.2    Powers and Duties.  The Chairman of the Board shall preside
                    -----------------
at all meetings of the stockholders and of the Board of Directors at which he is
present.  The Chairman of the Board shall also have such additional powers and
duties as may be prescribed for such offices from time to time by the Board of
Directors.  The President shall be the chief executive officer of the
Corporation.  In the absence of the President, an officer appointed by the
President, or if the President fails to make such appointment, by the Board of
Directors, shall perform all the duties of the President.  The officers and
agents of the Corporation shall each have such powers and authority and shall
perform such duties in the management of the business, property, and affairs of
the Corporation as generally pertain to their respective offices, as well as
such powers and authorities and such duties as from time to time may be
prescribed by the Board of Directors.

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                                  ARTICLE IV

                     RESIGNATIONS, REMOVALS AND VACANCIES

     Section 4.1    Resignations.  Any director or officer of the Corporation,
                    ------------
or any member of any committee, may resign at any time by giving written notice
to the Board of Directors, the Chairman of the Board, the President or the
Secretary of the Corporation.  Any such resignation shall take effect at the
time specified therein or, if no time is specified therein, then immediately
upon receipt thereof.  Unless otherwise specified in such notice, the acceptance
of such resignation shall not be necessary to make it effective.

     Section 4.2    Removals.  The Board of Directors, at any meeting thereof,
                    --------
or by unanimous written consent, at any time, may, to the extent permitted by
otherwise applicable Delaware law, remove with or without cause from office or
terminate the employment of any officer or member of any committee and may, with
or without cause, disband any committee.

     Section 4.3    Vacancies.  Any vacancy in the office of any officer through
                    ---------
death, resignation, removal, disqualification or other cause may be filled at
any time by the Board of Directors and, subject to the provisions of this
Article IV, the person so chosen shall hold office until his successor shall
have been elected and qualified.

                                   ARTICLE V

                                 CAPITAL STOCK

     Section 5.1    Stock Certificates.  The certificates for shares of the
                    ------------------
capital stock of the Corporation shall be in such form as shall be prescribed by
law and approved, from time to time, by the Board of Directors.

     Section 5.2    Transfer of Shares.  Shares of the capital stock of the
                    ------------------
Corporation may be transferred on the books of the Corporation only by the
holder of such shares or by his duly authorized attorney, upon the surrender to
the Corporation or its transfer agent of the certificate representing such stock
properly endorsed.

     Section 5.3    Fixing Record Date.  In order that the Corporation may
                    ------------------
determine the stockholders entitled to notice of or to vote at any meeting of
stockholders or any adjournment thereof, or entitled to express consent to
corporate action in writing without a meeting, or entitled to receive payment of
any dividend or other distribution or allotment of any rights, or entitled to
exercise any rights in respect of any change, conversion, or exchange of stock,
or for the purpose of any other lawful action, the Board of Directors may fix,
in advance, a record date, which, unless otherwise provided by law, shall not be
more than sixty nor less than ten days before the date of such meeting, nor more
than sixty days prior to any other action.  If no record date is fixed: (i) the
record date for determining stockholders entitled to notice of or to vote at a
meeting of stockholders shall be at the close of business on the day next
preceding the day on which notice is given, or, if notice is waived, at the
close of business on the day next preceding the day on which the meeting is
held; (ii) the record date for determining stockholders entitled to express

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consent to corporate action in writing without a meeting, when no prior action
by the Board of Directors is required under the DGCL, shall be the first day on
which a signed written consent setting forth the action taken or proposed to be
taken is delivered to the Corporation by delivery to its registered office in
the State of Delaware, its principal place of business, or an officer or agent
of the Corporation having custody of the book in which proceedings of meetings
of stockholders are recorded; and when prior action by the Board of Directors is
required under the DGCL, the record date for determining stockholders entitled
to consent to corporate action in writing without a meeting shall be at the
close of business on the date on which the Board of Directors adopts the
resolution taking such prior action; and (iii) the record date for determining
stockholders for any other purpose shall be at the close of business on the day
on which the Board of Directors adopts the resolution relating thereto. A
determination of stockholders of record entitled to notice of or to vote at a
meeting of stockholders shall apply to any adjournment of the meeting; provided,
however, that the Board of Directors may fix a new record date for the adjourned
meeting.

     Section 5.4    Lost Certificates.  The Board of Directors or any transfer
                    -----------------
agent of the Corporation may direct a new certificate or certificates
representing stock of the Corporation to be issued in place of any certificate
or certificates theretofore issued by the Corporation, alleged to have been
lost, stolen, or destroyed, upon the making of an affidavit of that fact by the
person claiming the certificate to be lost, stolen, or destroyed.  When
authorizing such issue of a new certificate or certificates, the Board of
Directors (or any transfer agent of the Corporation authorized to do so by a
resolution of the Board of Directors) may, in its discretion and as a condition
precedent to the issuance thereof, require the owner of such lost, stolen, or
destroyed certificate or certificates, or his legal representative, to give the
Corporation a bond in such sum as the Board of Directors (or any transfer agent
so authorized) shall direct to indemnify the Corporation against any claim that
may be made against the Corporation with respect to the certificate alleged to
have been lost, stolen, or destroyed or the issuance of such new certificates,
and such requirement may be general or confined to specific instances.

     Section 5.5    Beneficial Owners.  The person in whose name shares of stock
                    -----------------
stand on the books of the Corporation shall be deemed by the Corporation to be
the owner thereof for all purposes, and the Corporation shall not be bound to
recognize any equitable or other claim to or interest in such share or shares on
the part of any other person, whether or not it shall have express or other
notice thereof, except as otherwise provided by the laws of the State of
Delaware.

     Section 5.6    Regulations.  The Board of Directors shall have power and
                    -----------
authority to make all such rules and regulations as it may deem expedient
concerning the issue, transfer, registration, cancellation, and replacement of
certificates representing stock of the Corporation.

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                                  ARTICLE VI

                                 MISCELLANEOUS

     Section 6.1    Offices.  The Corporation shall maintain a registered office
                    -------
in the State of Delaware as required by law.  The Corporation may also have
offices in such other places, either within or without the State of Delaware, as
the Board of Directors may from time to time designate or as the business of the
Corporation may require.

     Section 6.2    Corporate Seal.  The corporate seal shall have inscribed
                    --------------
thereon the name of the Corporation, the year of its organization, and the words
"Corporate Seal" and "Delaware".

     Section 6.3    Fiscal Year.  The fiscal year of the Corporation shall be
                    -----------
determined and may be changed by resolution of the Board of Directors.

     Section 6.4    Notices and Waivers Thereof.  Whenever any notice whatsoever
                    ---------------------------
is required by law, the Certificate or these Bylaws to be given to any
stockholder, director or officer, such notice, except as otherwise provided by
law, may be given personally, or by mail, or, in the case of directors or
officers, by telegram, cable or facsimile transmission, addressed to such person
at his or her address as it appears on the books of the Corporation.  Any notice
given by telegram, cable or facsimile transmission shall be deemed to have been
given when it shall have been delivered for transmission and any notice given by
mail shall be deemed to have been given when it shall have been deposited in the
United States mail with postage thereon prepaid. Whenever any notice is required
to be given by law, the Certificate or these Bylaws, a written waiver thereof,
signed by the person entitled to such notice, whether before or after the
meeting or the time stated therein, shall be deemed equivalent in all respects
to such notice to the full extent permitted by law.

     Section 6.5    Amendments.  The holders of shares of capital stock entitled
                    ----------
at the time to vote in any general election of directors shall have power to
adopt, amend, or repeal the Bylaws of the Corporation by vote of the holders of
not less than a majority of the total voting power of the outstanding shares of
capital stock of the Corporation entitled to vote thereon, and except as
otherwise provided by law, the Board of Directors shall have power equal in all
respects to that of the stockholders to adopt, amend, or repeal the Bylaws by
vote of not less than a majority of the members of the Board of Directors then
in office.

     Section 6.6    Stock of Other Corporations or Other Interests.  Unless
                    ----------------------------------------------
otherwise directed by the Board of Directors, the Chairman of the Board, the
President, the Secretary, and such attorneys or agents of the Corporation as may
be from time to time authorized by the Board of Directors or the President,
shall have full power and authority on behalf of this Corporation to attend and
to act and vote in person or by proxy at any meeting of the holders of
securities of any corporation or other entity in which this Corporation may own
or hold shares or other securities, and at such meetings shall possess and may
exercise all the rights and powers incident to the ownership of such shares or
other securities which this Corporation, as the owner or holder thereof, might
have possessed and exercised if present.  The President, the Secretary, or such
attorneys or agents, may also execute and deliver on behalf of this Corporation
powers of attorney, proxies, consents, waivers, and other instruments relating
to the shares or securities owned or held by this Corporation.

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     Section 6.7    Savings Clause.  These Bylaws are subject to the provisions
                    --------------
of the Certificate and applicable law.  If any provision of these Bylaws is
inconsistent with the Certificate or the DGCL, such provision shall be invalid
only to the extent of such conflict, and such conflict shall not affect the
validity of any other provision of these Bylaws.

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