Vertical asymptotes result from a denominator equal to zero. So the denominator must include (x + 6) and (x + 3).
x-intercept are found when the numerator equals zero so the numerator must include (x + 2) and (x - 2).
So far we have f(x) = [(x + 2)(x - 2)]/[(x + 6)(x + 3)]
Both numerator and denominator have the same degree so the horizontal asymptote will be the leading coefficient of the numerator divided by the leading coefficient of the denominator. We can get a horizontal asymptote at y = 3 by just multiplying the numerator by 3. So: