First, if you can, Help > Deactivate or Help > Sign Out from the menu of PSE 12 on the old computer.
Download and install version 12 from here:
Help > Activate or Help Sign In and enter the PSE 12 serial number.
See here if you need to find the serial number:
It will ask you for the version 11 serial number if it was an upgrade. Enter it and you should be OK.