The axis of symmetry is y=-4, which means the parabola is lying on its side with arms pointing to the right.
The general equation for such a parabola is (y-k)²=4p(x-h) where (h,k) is the vertex, so h=k=-4. The focus lies on the axis of symmetry at (h+p,k).
Therefore h+p=-2, -4+p=-2, and p=2.
The equation of the parabola is:
(y+4)²=8(x+4) (answer c),
y²+8y+16=8x+32,
y²+8y-16=8x,
x=⅛y²+y-2.
In the picture the parabola is shown in blue with focus (green), vertex (red).
