Mr. Finman is running the hotel in Fishmouth.
Talk to him. Try to get a room. Talk until you learn his stomach is growling for food.
This is the low-spoiler guide for "Mr. Finman" puzzle in Gibbous - A Cthulhu Adventure. Unlike in normal walkthrough, you get gradual hints on how to solve the puzzle. Click the big button below to see your first hint. If the hint contains a spoiler, you will be warned about it before clicking.