2 - as long as they are not used at the same time
What are the computer operating systems involved? Are you installing from installation files (from online download purchase) or from installation disc
(from purchase in boxed packaging)? Answers to those questions would probably get you the best possible answer to your question.
If installation files.....
You are not going to be able to install a Premiere Elements Windows purchased serial number on a Mac computer or a Premiere Elements Mac
purchased serial number on a Windows computer.
If installation discs...
Box packaging typically comes with two installation discs....one for Windows and one for Mac. In this type of situation, typically you use one
serial number for them both. If that is the case, then the following applies...
Adobe allows you to use the same purchased activated serial number on no more than 2 of your computers. And, you do not use them at the same time.
If you are dealing with two computers with the same operating system, then you should be able to use that same purchased serial number for that operating system on no more than 2 of your computers. Again, you do not use them at the same time.
Please let us know if any questions or need clarification.