To solve $f(h(4))$, we need to follow these steps:

1. First, find $h(4)$:

   $h(x) = x + 1$ $h(4) = 4 + 1 = 5$

2. Next, find $f(h(4)) = f(5)$:

   $f(x) = 2x + 1$ $f(5) = 2(5) + 1 = 10 + 1 = 11$

So, the correct answer is C. 11.

Would you like any further explanation or have any questions? Here are five related questions to consider:

1. What is $f(h(2))$ given the same functions $f(x)$ and $h(x)$?
2. If $h(x)$ were $h(x) = 2x$, what would $f(h(4))$ be?
3. How do you find the composition of two functions in general?
4. What is the inverse of $f(x) = 2x + 1$?
5. How would the answer change if $h(x)$ were a different linear function?

Tip: When dealing with function composition, always start by evaluating the innermost function first.