Those carts should surely get you to the castle. But there is so much stuff to do before that.
This is the low-spoiler guide for "Getting to the castle" 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.