The Sukhothai region of has plenty of puzzles, but the ones associated with Khmer Cogwheels are directly tied to the main story.
Unlike optional Mystery quests, some of these puzzles must be solved to progress through the game. While you could stop after finding a couple of Cogwheel solutions, you can complete a few more for some rare rewards.
Unlike other Mysteries in that take place in a single location, the Khmer Cogwheel puzzles are scattered all across Sukhothai.
You have to travel to multiple places to collect Cogwheel items to unlock solutions for every puzzle. Doing so will allow you to move forward in the story and earn a rare achievement, along with other rewards that will help you get stronger.
The first time you'll find a Khmer Cogwheel is during quest in the main story. This takes place as you arrive at the Hidden Pyramid, a location near the northwest corner of the Sukhothai map.