Typically the equation of an ellipse is (x2/a2) + (y2/b2) = 1 where the vertices are (±a,0).
In this case that would make a=6.
The foci are (±ae,0) where e is the eccenticity = sqrt(a2 - b2)/a
In this case 6e = 3√3 => e = (1/2)√3
(1/2)√3 = sqrt(36 - b2)/6 => 3/4 = (36 - b2)/36 => 27 = 36 - b2 => b =3
Since you now have a and b, you know the equation for the ellipse which I gave you to start out.