Suppose $h(x)=f(g(x))$. Given the table of values below, determine $h^{\prime}(2)$. \begin{tabular}{|c|c|c|c|c|} \hline$x$ & $f(x)$ & $g(x)$ & $f^{\prime}(x)$ & $g^{\prime}(x)$ \\ \hline 2 & 6 & 3 & 0 & -4 \\ \hline 3 & 4 & 6 & 5 & -4 \\ \hline 5 & 4 & 4 & -2 & 3 \\ \hline \end{tabular} Do not include " $h^{\prime}(2)=$ "in your answer.

Step 1 ：Given the table of values for \(x\), \(f(x)\), \(g(x)\), \(f^{\prime}(x)\), and \(g^{\prime}(x)\), we are asked to find the derivative of the composite function \(h(x)=f(g(x))\) at \(x=2\).

Step 2 ：The derivative of a composite function is given by the chain rule, which states that \((f(g(x)))' = f'(g(x)) \cdot g'(x)\).

Step 3 ：From the table, we can see that \(g(2) = 3\), \(f^{\prime}(3) = 5\), and \(g^{\prime}(2) = -4\).

Step 4 ：Substituting these values into the chain rule gives us \(h^{\prime}(2) = f^{\prime}(g(2)) \cdot g^{\prime}(2) = 5 \cdot -4 = -20\).

Step 5 ：So, the derivative of the composite function \(h(x)=f(g(x))\) at \(x=2\) is \(\boxed{-20}\).