A project created in Premiere Elements 12 cannot be opened in Premiere elements 10.
But a project created in Premiere elements 10 can be opened in 12.
However if you exporting from premiere elements 12 as a video file you can import that video file in 10 and vice versa.
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GautmamBahl's reply is specific to the Project files, the .PREL's, and mirrors what most of us see, and experience.
However, if one were to Share a Timeline from PrE 10 to an output file, an AV file, that output file could be Imported into PrE 12 for additional editing. Some users, who move between versions of PrE (or even other editing programs) use that Share (now Publish+Share, and also Export in older versions) to get around the limitations of using the Project files, the .PREL's. They are basically producing what would be referred to as a DI, or Digital Intermediate file.
GautamBahl has already pointed out the difference to you between both project (project.prel file) versus an export from a project (video file).
And, I would confirm that you cannot open a Premiere Elements 12 project (project.prel file) in earlier versions such as 11, 10, and so on, and
you can open a Premiere Elements 10 project (project.prel file) in later versions such as 11 and 12. That type of situation is classic for Premiere Elements (all version, EXCEPT....)
And, the EXCEPT is specific to projects (project.prel files) created in Premiere Elements 10. Premiere Elements 10 projects (project.prel) can be opened in Premiere Elements 8.0/8.0.1. That same Premiere Elements 10 project (project.prel) cannot be opened in Premiere Elements 4, 7, or 9.0/9.0.1.
Although I am not recommending that you open a Premiere Elements 10 project.prel file in Premiere Elements 8.0/8.0.1, I did want to mention this one unexplained break in the classically answer to where project files from different versions can be opened.