We are given two functions: $f(t) = t^2 - t$ and $h(x) = 3x + 8$, and the task is to evaluate $h(f(2))$.

Step-by-Step Solution:

1. Evaluate $f(2)$:

   Using the given function $f(t) = t^2 - t$, substitute $t = 2$:

   $f(2) = 2^2 - 2 = 4 - 2 = 2$

2. Evaluate $h(f(2))$:

   Now that we know $f(2) = 2$, substitute $x = 2$ into the function $h(x) = 3x + 8$:

   $h(2) = 3(2) + 8 = 6 + 8 = 14$

Thus, $h(f(2)) = 14$.

Would you like a detailed explanation of any step?

Here are five related questions to extend your understanding:

1. How would the answer change if $f(t)$ were $t^2 + t$ instead of $t^2 - t$?
2. Can you find $h(f(-1))$?
3. What happens if the functions $f$ and $h$ are swapped, and we compute $f(h(2))$?
4. What does it mean to compose functions like in this problem?
5. How would you graph $h(f(x))$?

Tip: When evaluating compositions of functions, always work from the inside out!