Before you start moving things around, focus on what you need to accomplish first.
Start by finding a way to get the yellow block at the bottom into the hole currently occupied by the key.
If you feel like you're stuck, you might find it easier to just start over.
US Version
At the beginning, move the yellow block into the slot near the professor's hand. Next, take the square block on the right and move it to the left. After that, you need to find some way of moving that yellow block into the upper-right area of the puzzle.
UK Version
At the beginning, move the yellow block into the slot near the professor's hand. Next, take the square block on the right and move it to the left. After that, you need to find some way of moving that yellow block into the top-right area of the puzzle.
US Version
Once you've completed everything in Hint Two, you should be able to swap the key for that yellow block. Once you've put that yellow block in the slot the key was in, just shift all the other blocks and the key in one direction until the key is positioned at the bottom by the slot.
UK Version
Once you've completed everything in Hint 2, you should be able to swap the key for that yellow block. Once you've put that yellow block in the slot the key was in, just shift all the other blocks and the key in one direction until the key is positioned at the bottom by the slot.
Solution
Correct
Great work!
Now Luke and Professor Layton can finally leave the room!