This game is quite similar to Rubik's Cube, but it is a lot easier. Basically we should finish the puzzle row by row.

For ease of illustration, we label the tiles as follows:


You shouldn't have any problems finishing the first row:


To move the 5 to its correct position, follow the procedure: move down, move left or right, move up:


Do the same to move the 6 to its correct position:


Now you cannot do the same for the 7, because you will disrupt the 5 and 6. All we need is to modify the procedure slightly:


Follow similar steps to finish all the rows until there is only one row left:


We should swap the tiles in the last row until we finish. Suppose we arrive at the following situation:


Now we swap 15 and 16 first. Use the following formula:




Use a similar trick to swap 13 and 14 and we are done.