Can I transfer photoshop elements 12 from a windows 10 computer to a windows 11 computer

No. Win11 needs Photoshop Elements 2022 or higher. 

Elements 12 is way too old. 

https://www.adobe.com/products/premiere-elements/tech-specs.html

transfers of adobe apps almost always fail.  read ​@John T Smith ‘s reply and make sure you have your serial number handy.

You MAY be able to install, but only if you have not used up both activations

Two ideas that MAY work to install and/or run old programs in Windows 11
-RIGHT click the program icon or EXE and select a compatibility mode in the pop up option window
-and/or select Run as Administrator to assign FULL Windows permissions
-also https://helpx.adobe.com/x-productkb/global/create-local-administrator-account-windows.html

NOTE I have 4 very old IGT Slot games that I installed on Win11 (32bit x86 mode on 64bit OS)
I did not have to select a compatibility mode or run as Admin... Win11 just accepted them
So in my experience Microsoft has done a very good job with backwards compatibility
Program EXE dated 10-07-2015 Game of the Gods
Program EXE dated 03-06-2012 Diamond Galaxy
Program EXE dated 11-18-2011 Lucky Larry
Program EXE dated 08-04-2010 Wolf Run