Where/what did you originally purchase?
As far as I know, a download is computer specific... so if you bought a Windows download the serial number will not work for Mac
But, here is a download link so you may try for yourself Other downloads
Thank you for this link. Adobe offers Rel. 10 and Rel. 11 there but not Rel. 12
I do not know if the serial is valid for MAC also. I purchased a Windows version some month ago as download
Is your Mac computer strictly Mac or a Windows Mac combo?
If you purchased Premiere Elements 12 as an online download to your Windows 7 64 bit computer, you cannot use those files and that purchased serial number in a Mac computer operating system.
If you had purchased Premiere Elements 12 in box packaging from an authorized reseller, you would have received 2 installation discs, one for Windows and one for Mac. Then you would be in a good position now.
If you want Premiere Elements 12 Mac on your Mac computer, you are going to have to buy another license.
That is my take on your situation.
Any questions or need clarification, please do not hesitate to ask.