My guess
Can you explain why you limit the number of squares that can form a path to 16? Shouldn't it be 64-2=62.
The approach I took was a bit different.
assume the pawn starts from the bottom right square. According to the given condition he can move to any square on the board while reaching the target. The pawn has two options at each square except for the squares lying on the leftmost column and topmost row (see the attached image)
based on this: 2*(64-2-14)*14 is my answer.