I shouldn't assume you have learned L'Hopital's rule yet. Let me show you.
lim x-> - infinity (-7x^2-4x+16) / (-16x^2 + 3x + 3)
Plugging in infinity you get infinity/infinity which is L'Hop material
so take the derivative of the top and bottom
lim x-> - infinity (-14x-4) /(-32x+3) again infinity/infinity
take the derivative of the top and bottom again
lim x-> - infinity (-14/-32) = 7/16