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Related Party Transactions (Details) - Schedule of Allowance for Credit Loss Activity - USD ($) $ in Thousands | 3 Months Ended | 9 Months Ended | 12 Months Ended
--- | --- | --- | ---
Sep. 30, 2024 | Sep. 30, 2023 | Sep. 30, 2024 | Sep. 30, 2023 | Dec. 31, 2023 | Dec. 31, 2022
Schedule of Allowance for Credit Loss Activity [Abstract] |  |  |  |  |  |
Beginning balance |  |  | $ 2,087 |  |  |
Credit loss expense |  | $ 5,230 | $ 12 | $ 5,484 | 5,965 |
Balance deconsolidated with FCG |  |  |  |  | (3,878) |
Ending balance |  |  |  |  | $ 2,087 |

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- Definition Represent the amount of accounts receivable, allowance for credit loss. + References No definition available. + Details
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Namespace Prefix: | fbyd_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | instant

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- Definition Represent the amount of balance deconsolidated with FCG. + References No definition available. + Details
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Namespace Prefix: | fbyd_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | duration

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- References No definition available. + Details
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Namespace Prefix: | us-gaap_
Data Type: | xbrli:stringItemType
Balance Type: | na
Period Type: | duration

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- Definition Amount of interest income (expense) classified as nonoperating. + References Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef -Topic 220 -SubTopic 10 -Name Accounting Standards Codification -Section S99 -Paragraph 2 -Subparagraph (SX 210.5-03) -Publisher FASB -URI https://asc.fasb.org/1943274/2147483621/220-10-S99-2 Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef -Topic 280 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 22 -Publisher FASB -URI https://asc.fasb.org/1943274/2147482810/280-10-50-22 Reference 3: http://www.xbrl.org/2003/role/exampleRef -Topic 280 -SubTopic 10 -Name Accounting Standards Codification -Section 55 -Paragraph 48 -Publisher FASB -URI https://asc.fasb.org/1943274/2147482785/280-10-55-48 + Details
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Namespace Prefix: | us-gaap_
Data Type: | xbrli:monetaryItemType
Balance Type: | credit
Period Type: | duration