Cribbage Scoring Difficulties
First of all, there's only one fifteen: the seven and the eight.  That's two points.  (Note that the sixes can't participate in 15s at all)

Next, there are three runs of three: each six in turn, the seven, and the eight.  That's 3*3 = nine points.

Finally, there's the trio of sixes, worth six points (or equivalently, three pairs of sixes).

So the final score for the hand is 2+9+6 = 17 points.