A Premiere Elements hands on answer to your Premiere Elements question....
When your wrote "2 different computers", how different did you have in mind?
Adobe allows you to use the purchased activated serial number on no more than 2 of your computers. If you try to do otherwise,
you will get a message telling you that. But, the two are not to be run simultaneously.
That has been what has been posted here in the Premiere Elements Forum when such questions arise.
Just in case note, you cannot install Premiere Elements Windows installation files on a Mac computer and vice versa. Did you purchase Premiere Elements in box packaging where you had an installation disc for Windows and an installation disc for Mac. In that case, you would use the same serial number for each. But still, that same purchased activated serial number cannot be on more than 2 of your computers.
Please let us know if you have additional questions on this or need clarification.