Complete a glide reflection to the point H(-2, -3) with the translation (x, y) → (x – 2, y) and a reflection over y = -4.

To complete a glide reflection for the point \( H(-2, -3) \) using the translation \( (x, y) \rightarrow (x - 2, y) \) and a reflection over the line \( y = -4 \), we'll follow these steps:

1. **Apply the translation**:
The translation \( (x, y) \rightarrow (x - 2, y) \) transforms point H(-2, -3) as follows:

\[
H' = (-2 - 2, -3) = (-4, -3)
\]

2. **Reflect over the line \( y = -4 \)**:
To reflect the point \( H'(-4, -3) \) over the line \( y = -4 \), we need to find the distance from \( H' \) to the line \( y = -4 \).

- The y-coordinate of \( H' \) is \(-3\).
- The line \( y = -4 \) is below \( H' \) (since \(-3 > -4\)).
- The distance from \( H' \) to the line \( y = -4 \) is:

\[
\text{Distance} = -3 - (-4) = -3 + 4 = 1
\]

This means the reflected point \( H'' \) will be 1 unit below the line \( y = -4 \):

\[
H'' = (-4, -4 - 1) = (-4, -5)
\]

Hence, the point \( H'' \) after performing the glide reflection is:

\[
\boxed{(-4, -5)}
\]