What version of Turbo Tax 2024 can be run on an iMac running Monterey OS?

https://ttlc.intuit.com/community/system-requirements/help/minimum-system-requirements-for-turbotax-mac-software/00/25609

https://ttlc.intuit.com/turbotax-support/en-us/help-article/product-system-requirements/minimum-system-requirements-turbotax-windows/L8ZSsGqF1_US_en_US?uid=lph06daf

Sorry no.  You can’t install Turbo Tax 2024 on Mac with Monterrey 

2024 Desktop System Requirements

TurboTax® Desktop 2023-2024 System Requirements

If you can’t install the Desktop program you can switch to the Online version.  Then you can transfer your prior year returns from the Desktop program into the Online version.  You will have to get refund for the Desktop purchase and pay for Online separately.

If you used the Desktop program last year here’s How to transfer into the Online version, expand the blue link if you used the CD/download last year

https://ttlc.intuit.com/community/entering-importing/help/how-do-i-transfer-last-year-s-return-into-turbotax-online/00/25953

If you used the Desktop program before you may notice several differences and not like the online version.  It has less features and no Forms Mode.  You can only do 1 return.  Your return is only saved online so be sure to save both the .tax2024 data file and the pdf file to your computer when you are done.  In case you need to amend in the future or if you need a copy to get a loan or something.  You might not be able to access your online return when you need a copy.

Start an Online return here,

https://turbotax.intuit.com/personal-taxes/online/