Yes, you can install PSE12 on as many computers as you like, but only two can be activated (via Help> Sign In) at any one time. Only one should be in use at any time.
If your PSE12 was a full, rather than upgrade, version then there's nothing to stop you giving away PSE10. Remember to deactivate on your PC first (Help> Deactivate).
Insanity is hereditary, you get it from your children
If this post or another user's post resolves the original issue, please mark the posts as correct and/or helpful accordingly. This helps other users with similar trouble get answers to their questions quicker. Thanks.
Thank you for the help