This one is pretty fun. The ball spins around a bit, jumps up over a hoop, spins around, and so on. You want the ball to go back and forth and then out again without smashing into anything :)

While it's great fun to experiment, you want to stick the pegs into 12 white, 11 black, and 2 black. This gets you the final hex code to get up into the central mechanism.

The Myst 3: Exile Walkthrough