This puzzle is relatively easy for me to show you. Just place the blocks where I show them, and the path will be clear.

Step 2: Put one of the next two blocks in the pit, and the other we take across to the next pit.

Step 1: Easy so far

Step 3: Now we got an angle to place the next 2 blocks.

Step 4: Last block is in place, now we can push the barrel into the next area.

Step 5: Be careful not to push the crates over the edge, if you do you'll have to restart. Once they are out of the way (The way shown is one way, but you can do it several), then push the block to the South East into the pit to give yourself an angle on the barrel. Now just push the barrel in the west through the walkway (careful, if you knock it over the edge you'll have to restart!) and eventually push it into the hole in the floor in the first room you entered.