Answer
$$4y-8$$
Work Step by Step
Recall, one never divides by a fraction. Rather, if we want to divide by a fraction, we multiply by the reciprocal of the fraction. Recall, the reciprocal of a fraction is that fraction with the numerator and the denominator switched. Thus, we find:
$$ \frac{4y-8}{y+2}\div \frac{y-2}{y^2-4}\\ \frac{4y-8}{y+2}\times \frac{y^2-4}{y-2}\\ \frac{4y-8}{y+2}\left(y+2\right)\\ \frac{\left(4y-8\right)\left(y+2\right)}{y+2}\\ 4y-8$$