Let's solve each function and evaluate the expressions in the puzzle step by step:

Given functions:

1. $f(x) = 2x^2 - 8$
2. $h(x) = 3x - 10$
3. $g(x) = -2x^3 + x$

Step 1: Evaluate $f(-3)$

$f(x) = 2x^2 - 8$ Substitute $x = -3$: $f(-3) = 2(-3)^2 - 8 = 2(9) - 8 = 18 - 8 = 10$

Step 2: Evaluate $g(-3)$

$g(x) = -2x^3 + x$ Substitute $x = -3$: $g(-3) = -2(-3)^3 + (-3) = -2(-27) - 3 = 54 - 3 = 51$

Step 3: Evaluate $h(-8)$

$h(x) = 3x - 10$ Substitute $x = -8$: $h(-8) = 3(-8) - 10 = -24 - 10 = -34$

Step 4: Evaluate $g(2)$

$g(x) = -2x^3 + x$ Substitute $x = 2$: $g(2) = -2(2)^3 + 2 = -2(8) + 2 = -16 + 2 = -14$

Final Results:

1. $f(-3) = 10$
2. $g(-3) = 51$
3. $h(-8) = -34$
4. $g(2) = -14$

The corresponding numbers are: I, A, E, G.

The 4-letter code is: IAEG.

Do you want any more details or have any questions? Here are 5 related questions you might consider:

1. What happens if $x = 0$ for each function?
2. How does each function behave as $x \to \infty$?
3. Can we find the roots of $f(x) = 0$?
4. What type of function is $g(x)$ and how does its degree affect its shape?
5. What are the domains and ranges of each function?

Tip: Always double-check your arithmetic when substituting values to avoid small mistakes!