We are given a line segment $XY$ with coordinates $X(-8, -12)$ and $Y(p, q)$. The midpoint of $XY$ is $(-4, -2)$. We need to find the coordinates of $Y$, i.e., find the values of $p$ and $q$.

1. Problem Description

We are given a line segment $XY$ with coordinates $X(-8, -12)$ and $Y(p, q)$. The midpoint of $XY$ is $(-4, -2)$. We need to find the coordinates of $Y$, i.e., find the values of $p$ and $q$.

2. Solution Steps

The midpoint formula states that the coordinates of the midpoint $M$ of a line segment with endpoints $(x_1, y_1)$ and $(x_2, y_2)$ are given by:

$M = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})$

In our case, the coordinates of $X$ are $(-8, -12)$ and the coordinates of $Y$ are $(p, q)$. The midpoint is $(-4, -2)$. Applying the midpoint formula, we have:

$(-4, -2) = (\frac{-8 + p}{2}, \frac{-12 + q}{2})$

This gives us two equations:

$\frac{-8 + p}{2} = -4$

$\frac{-12 + q}{2} = -2$

Now, we can solve for $p$ and $q$:

$-8 + p = 2(-4)$

$-8 + p = -8$

$p = -8 + 8$

$p = 0$

And:

$-12 + q = 2(-2)$

$-12 + q = -4$

$q = -4 + 12$

$q = 8$

Therefore, the coordinates of $Y$ are $(0, 8)$.

3. Final Answer

(0, 8)

So, the answer is B.