The object of this puzzle is to interchange the white and the black pegs (golf tees). The rules are 1) you can move to a hole that's next to a peg; 2) you can jump, but only one peg and it must be of the other color, and 3) you can't move backwards. You must start with the empty space in the middle and end that way.
I have heard that this puzzle leads to a quadratic function.
Quadratic function games
So first of all you have to realize that except at the ends, you have to never end up with two same-coloured pegs next to each other. Then just go ahead and do it :-)