For those wondering:

• The first step is to factor. x² + x - 12 = (x+4)(x-3) and x² - 16 = (x+4)(x-4)
• That gives us g(x) = (x+4)(x-3) / (x+4)(x-4), which has two discontinuities: x=-4 and x=4
• We can simplify by canceling out x+4 from the numerator and denominator, giving us (x-3)/(x-4)
• We can see that there is still a discontinuity at x=4. This is going to be an asymptote, but that’s not the discontinuity we want right now.
• If we plug in x=-4, we get (-4-3)/(-4-4) = -7/-8 = 7/8, which is our limit, so the answer is A, limit = 7/8