Getting stuck in Riddle School usually means you missed an item or a dialogue clue. Here is how to keep your escape moving forward.
Click everything in every room. Items in Riddle School are not always obvious. A seemingly decorative object might be collectible, and a background detail might contain a clue. Thorough exploration prevents the frustration of backtracking later when you realize you missed something.
Talk to every NPC, even if they seem unimportant. Characters in Riddle School often drop hints about what items you need or where to use them. A throwaway comment about a broken vending machine tells you exactly where that coin in your inventory belongs.
Try using items on everything when you are stuck. The game has a limited number of interactive objects, so systematically trying your inventory items on each one in Riddle School will eventually reveal the correct combination. It is not elegant, but it works.
Pay attention to locked doors and blocked paths. These are your objectives. Every locked door in Riddle School has a corresponding key or mechanism somewhere in the school. Working backward from the obstacle to the solution is often easier than working forward from your current items.
If you are completely stuck, revisit rooms you have already cleared. New items sometimes become available after you complete certain actions elsewhere in the school. A room that had nothing useful on your first visit in Riddle School might contain the exact item you need after triggering an event in another location.