There seems to be a recurring confusion between product keys and the Laminar Identity when activating a copy of X-Pane 12.
If you have registered for a laminar identity, your Product Key is converted into an identity and you can activate X-Plane with your newly created User Name and Password associated with your identity. If you have not created a Laminar identity yet, you can activate X-Plane using your product key. If you have created an identity then the product key does not seem to work and you HAVE to activate using your identity.
If you have lost your product key, click here
For more information, there is a long thread on X-Plane.org here which should answer all your activation questions