Are you on the Internet when you start PSE? PSE12 requires that you should be online when you first install and use it. This way the product gets activated and the trial notice disappears.
Also, make sure that when you are exiting the product after you have finished what you are doing, DON'T LOGOFF from the PSE. IF you do then the trial message will come back again until login again. I know this is silly but this is the way Adobe has done it.
So in short, be online and login once if you haven't. That is all to it. I am assuming you have already entered the serial number so the activation would be automatic.
I looked at my list of adobe products that I have and it is listed by the correct serial number. but has mul under the platform as all my other products have win.
Mul means that the serial number you have will work with both Windows and Mac systems (this is the norm with retail boxed products). Those that say 'win' I would guess are downloaded versions - the norm here is that they are platform specific (in your case Windows).
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