If $h(x)=\sqrt{3+2 f(x)}$, where $f(4)=3$ and $f^{\prime}(4)=2$, find $h^{\prime}(4)$. $h^{\prime}(4)=\frac{a}{b}$, where $a$ is - and bis -. Write a comma - separated list.

Step 1 ：We are given the function $h(x)=\sqrt{3+2 f(x)}$, where $f(4)=3$ and $f^{\prime}(4)=2$. We are asked to find $h^{\prime}(4)$.

Step 2 ：We will use the chain rule of differentiation, which states that the derivative of a composite function is the derivative of the outer function times the derivative of the inner function.

Step 3 ：In this case, the outer function is $\sqrt{x}$ and the inner function is $3+2f(x)$.

Step 4 ：The derivative of the outer function is $\frac{1}{2\sqrt{x}}$ and the derivative of the inner function is $2f^{\prime}(x)$.

Step 5 ：Substituting these into the chain rule gives $h^{\prime}(x)=\frac{1}{2\sqrt{3+2f(x)}} \cdot 2f^{\prime}(x)$.

Step 6 ：We know that $f(4)=3$ and $f^{\prime}(4)=2$, so substituting these values in gives $h^{\prime}(4)=\frac{1}{2\sqrt{3+2\cdot3}} \cdot 2\cdot2$.

Step 7 ：Simplifying this gives $h^{\prime}(4)=\frac{2}{3}$.

Step 8 ：So, the final answer is \(\boxed{2,3}\).