16Standard equation of ellipse centre (h,k): (x-h)^2/a^2+(y-k)^2/b^2=1.
(h,k)=(-2,2) so (x+2)^2/a^2+(y-2)^2/b^2=1.
The end of the x semi-axis is (0,2) which is 2 to the right of centre (-2,2) so a=2.
When x=-2, y=6 (vertex), so 16/b^2=1 and b^2=16.
The equation is therefore (x+2)^2/4+(y-2)^2/16=1.
This can be written: 4(x+2)^2+(y-2)^2=16.