To give a safe answer, best to know what was the old computer operating system, what is the new one, and did you purchase an online download to the old computer from Adobe or did you install to the old computer via an installation disc from boxed packaging of the product.
The generalized answer is you deactivate Premiere Elements 12 on the old computer (Help Menu/Sign Out). It is up to you after that if you want to uninstall the deactivated program from the old computer. Deactivation is not the same as uninstall.
Then assuming no little technical complications of details, you install Premiere Elements 12 on the new computer using
a. Installation files that you saved to your computer or that you have download from "My Orders" at Adobe
b. Installation disc from boxed packaging.
Please fill in more details so we do not fall into any unexpected technicalities.