If you purchased Premiere Elements 12 from Adobe, you should be able to go to http://www.adobe.com, Sign In, and then go to My Products where your Premiere Elements 12 should be listed along with its serial number.
This is not Adobe. Just a user to user forum.
If you do not find your serial number under My Products at Adobe, there are two paths that you can follow:
Click on the following link, and, when it opens, click on the statement "Still Need Help? Contact us." to bring up the Adobe Chat to discuss your Order under the topic of
Orders, Refunds, and Exchanges.
Please let us know the outcome.
You can use the same link above to contact Adobe Chat about topic of product Activation under the topic of Serial number issues or Activating My Product.