Finding horizontal asymptotes of rational functions:
A horizontal asymptote is found by taking the limit of $y$ as $x \to \pm\infty$:
$\lim_{x \to \pm\infty} y = \lim_{x \to \pm\infty} \frac{-8}{x^2 - 4} = 0$.
Since the degree of the numerator (degree 0) is less than the degree of the denominator (degree 2), the line $y = 0$ (the x-axis) is the horizontal asymptote.

Option breakdown:

• $y = 0$ is the correct horizontal asymptote as $x \to \pm\infty$.
• $y = 8$ comes from the numerator constant.
• $y = 4$ comes from the denominator constant.
• $y = 2$ is incorrect; vertical asymptotes occur at $x = \pm 2$.