46-Step Solution
This puzzle has a long history (dates back to Victorian times), and it is known that it can be finished in 46 moves.
For ease of presentation, the positions are named as follows:

First, make 23 moves by moving the tiles at the following positions:
10, 8, 7, 9, 12, 6, 3, 9, 15, 16, 10, 8, 9, 11, 14, 12, 6, 5, 8, 2, 1, 7, 9
After that, the board will become as follows:

At this point, produce a "mirror image" of the above steps to finish the puzzle:
11, 17, 16, 10, 13, 12, 6, 4, 7, 9, 10, 8, 2, 3, 9, 15, 12, 6, 9, 11, 10, 8, 9
For ease of presentation, the positions are named as follows:

First, make 23 moves by moving the tiles at the following positions:
10, 8, 7, 9, 12, 6, 3, 9, 15, 16, 10, 8, 9, 11, 14, 12, 6, 5, 8, 2, 1, 7, 9
After that, the board will become as follows:

At this point, produce a "mirror image" of the above steps to finish the puzzle:
11, 17, 16, 10, 13, 12, 6, 4, 7, 9, 10, 8, 2, 3, 9, 15, 12, 6, 9, 11, 10, 8, 9
Click the button below to play this game now: