It this is subscription there is no serial number. Just your Adobe ID
Out of curiosity, why would you choose to use Photoshop CS6 if you have a subscription?
In any case, if you were using a serialized version of the software or updated the trial to the latest release, you may well have to uninstall it and reinstall it via the Creative Cloud application, because you may have been following the serialized upgrade path vs. the subscription upgrade path. Yeah, it's complicated.
What do you see in the Creative Cloud application for the status of your installed software? Feel free to post a screen grab.