your new computer may come with an app to move documents like  xxxx.tax2021 to your new computer.  if not then you can use a thumb drive to move it from the MAC to the thumb drive and from there to the new PC. another method is you can attach the file to an e-mail from yourself on the MAC to your PC e-mail account

note that an e-mail is only as secure as your email in general.

BEFORE you lose access to the prior year returns ... if you have not yet saved all the prior year returns as both a PDF and a .taxfile then  do so now so you can open the return in the future if needed.

Then the WIN 2022 program will be able to transfer the 2021 tax file from the MAC machine without issue.

You can't transfer the programs.  They have to be installed from the CD or Download.  You don't need to install the prior year programs unless you need to amend that year.  Before you move your tax return files make sure you have saved each year as a PDF file.  So you may want to open each year and do that.  FILE - SAVE TO PDF

What I would do is just copy the whole Turbo Tax folder that is under your Documents.  That should be where the .tax files and PDF files are stored.  Then copy that folder to a flash drive or best yet is to burn it to a CD or DVD and then you will have a backup of them.   Then on the new computer copy the folder (or files) from the flash drive to your Documents folder.  Those can always be at least read by any system, even if they can't be used directly by the program.

Save the PDF for each year twice.

1) Once as the tax return for filing   (this contains just the filing tax forms)

2) Again as the tax return, but with ALL the forms and worksheets (this contains all of your worksheets and shows all  of your entries on some form or another).

The selection of the bare tax return, or the extended tax return with everything is made during the Save-to-PDF process.

And back those PDFs up to a backup USB or CD....every year we get tons of folks begging for access to a tax return on a crashed disk....TTX doesn't have it...only you do when you use the desktop software.

See this TurboTax support FAQ concerning moving tax files to a new computer - https://ttlc.intuit.com/questions/1901474-how-do-i-move-my-tax-data-file-to-another-computer

This is my mini version of  a tutorial  that should be in the downloaded program: 

What is Forms Mode?

Forms Mode lets you view and make changes to your tax forms "behind the scenes."

If you're adventurous, you can even prepare your return in Forms Mode, but we don't recommend it. You may miss obscure credits and deductions you qualify for, and you may forget to report things that will come back and haunt you later.

Forms Mode is exclusively available in the TurboTax CD/Download software. It is not available in TurboTax Online.

Related Information:

• Why would I use Forms Mode?
• How do I switch to Forms Mode in the TurboTax for Windows software?
• How do I switch to Forms Mode in the TurboTax for Mac software?
• What is-the-meaning-of-all-the-different-colors-in-forms-mode

If you want to play around with different figures and tax scenarios without affecting your original return you can ….

• >>>In the TurboTax CD/Download software by creating a test copy: 
• 1.  Open your return in TurboTax. 
• 2.  From the File menu, choose Save As. 
• 3.  Give the copy a new name to distinguish it from the original (for example, by adding "Test" or "Example" to the file name). 
• 4. Click  Save. You are now safely working in the test copy and anything you do here will not affect the original. 
•  https://ttlc.intuit.com/questions/1900642-how-to-make-a-test-copy-of-your-return

• >>  use the WHAT IF tool: 
• - Click Forms Icon (upper right of screen) or Ctrl 2 (forms view) 
• - Click on the Open Form Icon 
• - In the “Type a form name.” area type What-If (with the dash), click on the name of the worksheet - click on Open Form 
• - You will see the worksheet on the right side of the screen; enter the information right into the form 
• - To get back to interview mode - click on the Step-by-Step Icon (upper right of screen) or Ctrl 1

Once you have filed successfully … you can shut off the auto updater function and then save the return &  .taxfile.

It's always a good idea to make a backup copy of your tax data file, in case your original gets lost or corrupted. Here's how:

1. From the File menu in the upper-left corner of TurboTax, choose Save As (Windows) or Save (Mac).
2. Browse to where you want to save your backup.
   • Tip: If you're saving to a portable device, save it to your computer first to prevent data corruption. Then, after completing Step 4, copy or move the backup file to your device.
3. In the File name field, enter a name that will distinguish it from the original tax file (for example, add "Backup" or "Copy" to the file name)
4. Click Save and then close TurboTax.
5. Restart TurboTax and open the backup copy to make sure it's not corrupted. If you get an error, delete the backup and repeat these steps.

If you make changes to your original tax return file, repeat these steps to ensure your original and backup copies are in-synch.

Related Information:                             

• Retrieve a Tax File from a Portable Device
• What's the difference between the tax data file and the PDF file?

AND save it as a PDF so you have access to a copy even if you don’t have the program still installed and operational :

• How do I save my return as a PDF in the TurboTax software for Windows?
• How do I save my return as a PDF in the TurboTax software for Mac?

AND protect the files :

• How can I protect the tax files on my computer?

*** Other clues to the downloaded program ***

In the forms mode ... double click  or right click on a box on a form to data source it ... sadly it doesn't work on all boxes. 

What's the meaning of all the different colors in Forms Mode?

When you look at an onscreen tax form using Forms Mode, you might wonder why one figure is blue and the one next to it is red or black.

These colors indicate the source of that data.