In this maze, you must remember not only where you are, but what type of move you did last. Pretend that the boxes are cards laying on top of each other. If you just went from a “lower” card to a “higher” card, we say you just went up. Similarly, if your last move was from a “higher” card to a “lower” card, then your last move was down. If your last move was up, then your next move must be down, and if your last move was down, then your next move must be up. Thus your entire sequence of moves will be START, down, up, down, up, down, up, down, …, FINISH.
These sort of mazes are called “multi-state” mazes. In most mazes you have only 1 state (your position in the maze) that completely determines what you can do. Here you have 2: position, and what your last move was.
One interesting property of these mazes is that you can loop around to somewhere you have been before, but have a completely different set of available moves than the last time you were there.