Question 28577
It is not solvable.  It takes 7 swaps of adjacent pairs to "solve" it.  Since 7 is an odd number, it is not solvable.  If it took an even number of swaps, it would be solvable.
Note:
In the first row, swap 2 and 1.
In the third row, swap 11 and 12.
In the 4th row, 15,13,14 --> 13, 15, 14 --> 13,14,15 (2 swaps)
In the second row, 5, 8, 7, 6 --> 5, 7, 8, 6 --> 5, 7, 6, 8 --> 5, 6, 7, 8 (3 swaps).
That's 7 swaps altogether.

To try it out, go to http://www.javaonthebrain.com/java/puzz15/.  You can get everything down to a single pair out of order, but no further.