From Jade's guide.
The word you need to spell is "open". Right above you is the letter n. For the sake of getting it out of the way, I always push it north once, then right once so it's against the wall. Put it there, and you'll be able to move around it on all sides that matter. I just don't like it being right near the door you came through, as it's possible to step out the door and reset the whole puzzle if you're not careful. So the letter N is placed.
The letter E is far west and a bit north of where your N is placed, and you might find O when you're over there. E is just to the northeast of O. Push E to the east about eight steps, then get above it and push it down three times. At this point it ought to be lined up with your N, but if you want to be sure, get on the right side of the letter E and move right. If you bump the n, then double back west and bump the E, you're in business. In that case, get around to the left side of the E and push it to the right until it bumps something. That's two letters done.
The P is nearby, just to the northwest. Push it down three spaces, get around to its west side, then push it east twice. That should make three letters. You only have an O left.
The O is, if you'll remember, off to the west, near where the E was. Go that way, and you'll find it. Push it down once if you're following my directions, then shove it all the way east until you hear a cracking, breaking noise. This is the door unlocking, so feel free to go north through the now-unbarricaded door.
This strategy works for me as well. I cover this in my playthrough, which everyone will have access too in the next couple days.