Over the course of the chapters, we learn that by burning Primrose's books, Megan will become possessed by a demon. During the finale, you will need to free her by saying the demon's name - Metum. If you did not use the name during the chapters, you will need to search the nearby bookcase to learn the name.
To complete the quest, you will need to give her a Note from gail, found by the Needle.
If you did not unlock all the keywords during the quest, you will be able to use the Shard of the needle to discover them after. You will need to speak with Megan to obtain any new rewards that you earn.