What is the equation of a parabola with (−2, 4) as its focus and y = 6 as its directrix?

Well it is concave down with a focal length of 1 and the vertex at (-2,5)

so

\((x-h)^2=4a(y-k)\\ (x+2)^2=4*-1*(y-5)\\ (x+2)^2=-4(y-5)\\\)