If you bought the boxed product, there should be both versions on discs inside the box
If you bought the download version, I think you have to buy again (not 100% sure about that, I don't buy via download... check the Adobe product site)
The answer to your question hinges on what you purchased.
If you purchased an online download with serial number from Adobe to your Windows computer, all that you purchased was Premiere Elements 12 specific to the computer operating system to which it was downloaded...in this case, some version of Windows. So, you would have to purchase Premiere Elements 12 Mac/serial number for your Mac computer.
If you purchased the boxed packaging of Premiere Elements 12, you should have 2 installation discs as part of that one purchase...one disc Windows installation and one disc for Mac installation. Each will have the same serial number.
Looking forward to your comments to confirm which reply applies to your situation.
I purchased the download version
Thanks for the reply.
You should not be able to use those Premiere Elements 12 Windows downloaded installation files on the Mac.
How long ago did you purchase Premiere Elements 12 Windows from Adobe. If purchased from Adobe, you should be able to get your money back within 30 days of purchase.
Then you can consider what next, for example, purchase the boxed packaged product from an authorized reseller. Adobe sells only the download, not the boxed packaging, for Premiere Elements 12. The boxed packaging will contain a Premiere Elements 12 installation disc for Windows and one for Mac.
If you need to double check any of this information, you could try to contact Adobe via its Adobe Chat to discuss Downloading, Installing, and Setting Up. To do that, click on the following link, and, when it opens, click on the question "Still Need Help? Contact Us." to bring up the Adobe Chat.
Please let us know the outcome when you get a chance.