The problem asks us to evaluate the polynomial function $h(x) = 2x^4 - x^3 + 2x^2 - 3x - 4$ at $x = -1$. In other words, we need to find $h(-1)$.

1. Problem Description

The problem asks us to evaluate the polynomial function $h(x) = 2x^4 - x^3 + 2x^2 - 3x - 4$ at $x = -1$. In other words, we need to find $h(-1)$.

2. Solution Steps

To find $h(-1)$, we substitute $-1$ for $x$ in the polynomial:

$h(-1) = 2(-1)^4 - (-1)^3 + 2(-1)^2 - 3(-1) - 4$

Now, we simplify each term:

$(-1)^4 = 1$

$(-1)^3 = -1$

$(-1)^2 = 1$

So,

$h(-1) = 2(1) - (-1) + 2(1) - 3(-1) - 4$

$h(-1) = 2 + 1 + 2 + 3 - 4$

$h(-1) = 8 - 4$

$h(-1) = 4$

3. Final Answer

4