This problem is a direct application of the chain rule. There is an "outside" ($f$), "middle" ($g$), and "inside" ($h$). The chain rule tells us to work our way from the outside in, taking derivatives along the way, always leaving the stuff on the inside alone. I'll get you started:

(1)
\begin{align} k'(2)=f'(g(h(2)))\cdot (\text{middle}')\cdot (\text{in}') \end{align}

Figure out what $\text{middle}'$ and $\text{in}'$ are and then plug the given information in (working inside out if necessary).

By the way, I cooked up this problem so that it would be the "answer to everything."