Plot those 4 intercepts:

 draw the ellipse 

Since it looks like this: "" 
and not like this:"",

its equation is

 +  = 1

The center is (h,k) = (0,0), so it has the form

 +  = 1

 +  = 1

The y-intercepts are the vertices, the x-intercepts are the covertices:
                                                               _
a = semi-major axis = distance between center and a vertex = 2Ö3

Therefore 
                                                                _
b = semi-minor axis = distance between center and a covertex = Ö6
                  _                       _
Therefore a² = (2Ö3)² = 4·3 = 12,  b² = (Ö6)² = 6

 +  = 1

Edwin