For the Elements 12 family you can install PSE/PRE on as many machines as you like, but only two can ever be signed in at one time (sign in is the new activation method in Elements 12).
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What version of Premiere Elements is involved and on what computer operating system is involved?
What are you using for the install - installation files from a purchased download of the program or installation disc from purchased of program in boxed packaging? If you have purchased installation files from a download, your installation files may be specific to the computer operating system to which the files were downloaded. Needs to be explored with regard to the computer 1 and computer 2 operating systems.
Classically, Adobe allows for the purchased activated serial number to be used on no more than 2 of your computers and not used at the same time.
If more than 2 computers have an installed activated copy of the same serial number, deactivation of one of those serial numbers would be required if you want to install the program on a 3rd computer. Deactivation is not the same as uninstall and needs to be done before any uninstall. In Premiere Elements 11 and earlier, deactivation is done in Help Menu/Deactivate. The counterpart of that for deactivation in Premiere Elements 12 is Help Menu/Sign Out. You do not have to uninstall a deactivated program on a computer.
Please let us know if you need clarification on anything written. Additional details would help us fine tune the reply.