When you open Lightroom6(Trial) it will pop up a message saying "Your Trial has expired/Days remaining"
Click on "License this software" on the Bottom Left.
Enter your Serial number.
Product will be Activated.
Follow this link for step by step explanation Adobe Photoshop Lightroom Help | Serialize Lightroom CC trial to activate as Lightroom 6
Let us know if that helps
The box with trial has expired...no longer shows.
Now it says LR will open with reduced functionality...
Please open Lightroom >>Help>>Sign Out
Restart Lightroom(Do not sign in)
Select License This Software
If it is still the same
Go to ~/Library/Application Support/Adobe/OOBE(MAC) C:\Users\Username\AppData\Local\Adobe\OOBE(Windows) *Appdata is hidden Folder
Rename the Opm.dbFolder to Opm.db.old
Then restart Lightroom