You cannot use Premiere Elements 12/12.1 Windows on Mac, and you cannot use Premiere Elements 12/12.1 Mac on Windows.
Also, you cannot open Premiere Elements 12/12.1 Windows projects in Premiere Elements 12/12.1 Mac and vice versa.
If you want to use Premiere Elements 12/12.1 on your Mac computer, I see no alternative but for you to find a seller who still has it in stock and purchase it.
Please review, consider, and then let us know if you have any questions or need clarification on this matter.
I thought that I could download it and use my old serial number. But i couldn´t, why?
First, this is not Adobe. Rather essentially user to user forum. Final word on anything Adobe comes from Adobe. But, you should get the same answer here as there on this.
If you purchased Premiere Elements as a download, what you purchased was specific to the computer operating system to which it was downloaded. And the serial number is specific to that purchase.
If you had purchased Premiere Elements in boxed packaging, then you get 2 installation discs, one for Windows and one for Mac.
Bottom line based on the details posted...: what you purchased was Premiere Elements 13 Windows license and not a license for Premiere Elements 13 Mac. If you need a Premiere Elements 13 Mac license, then you need to purchase it with its serial number.
Please consider. Any questions, please ask.