Did you purchase the product as a download from Adobe? If so, the download is specific to the operating system to which the download was downloaded.
So, if you downloaded the purchase to Mac, the purchase that you have will not work on Windows or vice versa.
If you purchased the product in boxed packaging you should have a installation disc for Windows and one for Mac.
Adobe allows you to use the same purchased activated serial number on no more than 2 of your computers. And, then you are supposed to use only one at a time. See Adobe Licensing Agreement.
Please give the details of your situation so that we can determine what of the above applies to your situation.
Also, project files created in Premiere Elements Windows cannot be used in Premiere Elements Mac and vice versa.