What version of Premiere Elements, what computer operating system?
For purposes of example, I will assume Premiere Elements on Windows 7, 8, 8.1, or 10 64 bit.
For Premiere Elements 12/12.1, 13/13.1, or 14, open the program to a new project, go to Help Menu/Sign Out.
That deactivates the program. If you do not want that version of Premiere Elements on your computer any longer, you can take the added step of uninstalling the program. Deactivation is not the same as uninstall.
For Premiere Elements 11, same thing except the Help Menu/ uses "Deactivate" instead of Help Menu/Sign Out.
Then you install Premiere Elements on your other computer, from installation files or installation discs.
Just in case mention...Premiere Elements Windows needs to be installed on Windows and Premiere Elements Mac needs to be installed on Mac. And, Premiere Elements Windows projects cannot be opened in Premiere Elements Mac.
Please consider. Any questions or need clarification on the above, please do not hesitate to ask.