We are given the function $h(x) = 4x + 3$. You are asked to find $h(4h(4))$. Let's break it down step-by-step:

Step 1: Find $h(4)$

Using the given function $h(x) = 4x + 3$, substitute $x = 4$:

$h(4) = 4(4) + 3 = 16 + 3 = 19$

Step 2: Find $h(4h(4))$

Now that we know $h(4) = 19$, we need to find $h(19)$ by substituting $x = 19$ into the function $h(x) = 4x + 3$:

$h(19) = 4(19) + 3 = 76 + 3 = 79$

Final Answer:

$h(4h(4)) = 79$

Would you like more details or have any questions?

Here are five related questions for further practice:

1. What is $h(5h(5))$ for the same function?
2. If $h(x) = 3x + 2$, how would you find $h(3h(3))$?
3. What is the inverse of the function $h(x) = 4x + 3$?
4. What is $h(h(x))$ for the function $h(x) = 4x + 3$?
5. How does the graph of $h(x) = 4x + 3$ look?

Tip: Always check intermediate steps in a nested function like this to avoid mistakes!