This puzzle becomes quite easy once you have mastered the basics.
For ease of presentation, the tiles are named as follows:
You should finish the puzzle from top to bottom and from left to right.
Moving tiles 1 and 2 to their positions shouldn't be a problem:
For the last two tiles in the first row, move the second last tile (tile 3) to the position of the last tile (position 4):
Move the last tile (tile 4) to the position below its correct position:
After that, finishing the first row will be easy:
Follow the same procedure 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: