No. You need 10.14 or newer.
Mac System Requirements
FYI - Switching to the Online version
If you can't install Turbo Tax Desktop program you can transfer from your 2019 return from your computer into the online version. You need to have the file ending in.tax2019 on your computer.
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
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 .tax2020 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/
Do I need to return the disk I bought to the store (opened and downloaded) ? Or can I use the license code at check out on the online version
No. You can't use the License Code for the Online version. Why can't you use the Desktop program on your computer? Did you get it installed?
No I can't upgrade past 13.6 on this iMac
but I did get it to work on mom's old PC, I'll just need to re-enter every thing by hand
thank for the help
You probably didn't need to start over. If you filled out the online version you can switch it to the Desktop program without paying for online.
First download the .tax file from the Online version,
Then see, How to Switch to Desktop,
After you get the program installed the first thing to do before you open your tax return is to update the program and install any state programs you had. So you first might need to start a fake return to be able to download the state program (go to FILE - New)
Then you just OPEN the .tax2020 file, go up to File-Open. You don't import or transfer it.