To find the value of the given expression:

$(-4x^2y - 5x^4 - 4y) + (-7y - 3x^2y + 2x^4),$

when $x = 3$ and $y = -2$, we will substitute the values into the equation step by step:

Step 1: Combine like terms

Combine terms with $x^2y$, $x^4$, and $y$:

$(-4x^2y - 3x^2y) + (-5x^4 + 2x^4) + (-4y - 7y).$

This simplifies to:

$-7x^2y - 3x^4 - 11y.$

Step 2: Substitute $x = 3$ and $y = -2$

Substitute the values of $x$ and $y$ into the simplified expression:

$-7(3^2)(-2) - 3(3^4) - 11(-2).$

Step 3: Calculate each term

1. $3^2 = 9$, so $-7(3^2)(-2) = -7(9)(-2) = 126$,
2. $3^4 = 81$, so $-3(3^4) = -3(81) = -243$,
3. $-11(-2) = 22$.

Step 4: Add the results

$126 - 243 + 22 = -95.$

Final Answer:

The value of the expression is:

$\boxed{-95}.$

Do you want a detailed explanation or have further questions? Here are some follow-up queries you might explore:

1. How do we combine like terms in more complex expressions?
2. Why is the order of operations critical when simplifying such problems?
3. Can we graph this expression with variable values for $x$ and $y$?
4. How does substitution simplify polynomial evaluation?
5. What happens if one variable is zero in this equation?

Tip: Always simplify an expression as much as possible before substituting values to reduce calculation errors.