ANSWER
[tex]{(y + 2)}^{2} = 8(x - 4)[/tex]
EXPLANATION
The given parabola has equation of the form
[tex] {(y - k)}^{2} = 4p(x - h)[/tex]
where (h,k) is the vertex of the parabola.
The vertex of the given parabola is (4,-2).
and p is the distance between the foci and the vertex.
[tex] |p| = 2[/tex]
The parabola opens towards the positive x-axis, therefore p=2.
Hence the equation of the parabola is
[tex] {(y + 2)}^{2} = 4 \times 2(x - 4)[/tex]
[tex]{(y + 2)}^{2} = 8(x - 4)[/tex]
