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Fair Value Measurement (Details) - Schedule of Unobservable Inputs of the Earnout Liability for Earnout Shares Based on Revenue and EBITDA Targets - $ / shares	9 Months Ended	12 Months Ended
	Sep. 30, 2024	Dec. 31, 2023
Schedule of Unobservable Inputs of the Earnout Liability for Earnout Shares Based on Revenue and EBITDA Targets [Abstract]
Current stock price (in Dollars per share)	$ 8.26	$ 10.25
Earnout period – beginning	Jul. 01, 2023	Jul. 01, 2023
Earnout period – end	Dec. 31, 2024	Dec. 31, 2024
Equity volatility, EBITDA volatility	30.00%	25.00%
Operational leverage ratio	65.00%	65.00%
Revenue volatility	10.00%	10.00%
Revenue/stock price correlation	40.00%	45.00%
EBITDA/stock price correlation	30.00%	25.00%
Revenue discount rate	14.27%	9.21%
Dividend yield	0.00%	0.00%

X

- Definition

Percentage of EBITDA stock price correlation.

+ References

No definition available.

+ Details

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Namespace Prefix:	fbyd_
Data Type:	dtr:percentItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Date of the earnout period beginnings.

+ References

No definition available.

+ Details

Name:	fbyd_EarnoutPeriodBeginnings
Namespace Prefix:	fbyd_
Data Type:	xbrli:dateItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Date of earnout period ending.

+ References

No definition available.

+ Details

Name:	fbyd_EarnoutPeriodEnding
Namespace Prefix:	fbyd_
Data Type:	xbrli:dateItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Percentage of equity volatility EBITDA volatility.

+ References

No definition available.

+ Details

Name:	fbyd_EquityVolatilityEBITDAVolatility
Namespace Prefix:	fbyd_
Data Type:	dtr:percentItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Percentage of revenue discount rate.

+ References

No definition available.

+ Details

Name:	fbyd_RevenueDiscountRate
Namespace Prefix:	fbyd_
Data Type:	dtr:percentItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Percentage of revenue volatility.

+ References

No definition available.

+ Details

Name:	fbyd_RevenueVolatility
Namespace Prefix:	fbyd_
Data Type:	dtr:percentItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Percentage of revenue stock price correlation.

+ References

No definition available.

+ Details

Name:	fbyd_RevenuestockPriceCorrelation
Namespace Prefix:	fbyd_
Data Type:	dtr:percentItemType
Balance Type:	na
Period Type:	duration

X

- References

No definition available.

+ Details

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Namespace Prefix:	fbyd_
Data Type:	xbrli:stringItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Percentage of investment income (loss) to average net assets.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 946
-SubTopic 205
-Name Accounting Standards Codification
-Section 50
-Paragraph 10
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147478494/946-205-50-10

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

X

- Definition

The estimated dividend rate (a percentage of the share price) to be paid (expected dividends) to holders of the underlying shares over the option's term.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (f)(2)(iii)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147480429/718-10-50-2

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	dtr-types:percentItemType
Balance Type:	na
Period Type:	duration

X

- Definition

Price of a single share of a number of saleable stocks of a company.

+ References

No definition available.

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	dtr-types:perShareItemType
Balance Type:	na
Period Type:	instant