The problem asks us to evaluate the function $g(x) = -2|4x - 8| + 3$ at $x = -4$. This means we need to find the value of $g(-4)$.

1. Problem Description

The problem asks us to evaluate the function $g(x) = -2|4x - 8| + 3$ at $x = -4$. This means we need to find the value of $g(-4)$.

2. Solution Steps

First, we substitute $x = -4$ into the expression for $g(x)$:

$g(-4) = -2|4(-4) - 8| + 3$

Next, we simplify the expression inside the absolute value:

$4(-4) - 8 = -16 - 8 = -24$

So we have:

$g(-4) = -2|-24| + 3$

The absolute value of $-24$ is $24$, so we have:

$g(-4) = -2(24) + 3$

Now, we multiply $-2$ by $24$:

$-2(24) = -48$

So we have:

$g(-4) = -48 + 3$

Finally, we add $-48$ and $3$:

$-48 + 3 = -45$

Therefore, $g(-4) = -45$.

3. Final Answer

$g(-4) = -45$