We use the form [tex](y-k)^2 = 4p(x-h)[/tex] when [tex](h,k)[/tex] is the vertex, p is the distance between the focus and the vertex. We know this because this is a parabola that opens to the left, along the x axis. The directrix is the same distance away from the vertex (in terms of its perpendicular line from it to the vertex) as the focus, so p = 9, since |-6 - 3| = 9 (perpendicular distance from directrix to vertex). We know the vertex is (-4,-6), so we apply all of these values to get the standard form:
[tex](x+4) = 36(y+6)^2[/tex]
