Answer:
Set the denom to 0 and solve.
x^2 - 16 = 0 --> x = -4,4
This means the vertical asymptote is 4, -4.
Therefor, the domain is for all real numbers that are not 4, -4.
We ignore the top because if the numerator was 0, it's still a number. But if the denom was 0, then it would be impossible (you can't divide by 0). So for all numbers that can go into the denom that aren't 0, is your domain.