The simple answer is to deactivate 10 from computer 1 (Help Menu/Deactivate). You not have to uninstall it at that point unless you want to. Deactivation and uninstall are not the same thing. Then install Premiere Elements 10 on computer 2. But, I do not have enough information from you to label this simple answer.
To whom is Premiere Elements 10 licensed - individual license or volume license? What computer operating systems are involved going from and to? Are these computers all on the same company network?
This is not Adobe. Rather essentially user to user forum.
From an Adobe License we read that the "customer" is allowed to use the purchased activated serial number on no more than 2 of his/her computers and then not use both at the same time.
The program needs to be run as administrator. And, the install might run into problems with antivirus and firewalls or other company security measures not disabled. Does your company have an IT person, or are you the IT person?
The transfer of license typically does not apply to deactivating, uninstalling the program and reinstalling it on another of your computers.
So what you describe sounds like moving a version from one computer to another. Do you have installation files or disc, and do you have a purchased serial number for your copy of Premiere Elements 10?
Caution...you do not want to be moving Premiere Elements 10 to a computer than uses a NVIDIA GeForce video card/graphics card.
It is a computer of the same network and of the exact same computer configuration. I have four licensed copies of the the program. Is there a way to see which serial number i am deactivating?
I am using an individual license model for this reply.
If you have Premiere Elements 10 installed on computer 1, you installed it with an Adobe ID and password (an Adobe Account) in the installation. That specific product is then likely to be registered at Adobe under your Adobe Account. Go to the Adobe web site
http://www.adobe.com, sign in with your Adobe ID and password, type My Products in the Search field there, and navigate to your "My Products". When at "My Products", look for the listing for Adobe Premiere Elements 10, click on it to reveal its serial number.
Depending on the number of Adobe IDs and passwords that you have and if all 4 of the licenses have been installed at one time or another, things can get complicated or you may find what you are looking for.
Lots of scenarios.