This puzzle becomes quite easy once you have mastered the basics:

For simplicity, we mark the tiles as follows:


We should finish the puzzle from top to down, and from left to right

Moving tile 1 and tile 2 to their positions shouldn't be a problem


For the last two tiles in the row, move the second last tile (tile 3) to the last position (position 4)


Move the last tile (tile 4) to the position below it's correct position


After that, finishing the first row will be easy


Follow the same pocedure to finish the remaining rows until there are 2 rows left:


Now, finish the remaining tiles column by column, starting from the right, using similar techniques




When there are only 4 tiles left, simply rotate the tiles and you will get the picture.