The standard form of a horizontal hyperbola is (x -h)^2/ a^2 - (y -k)^2/b^2 = 1. Since the vertices and foci of this hyperbola is horizontal.
Halfway between the vertices (or foci) will be the center. So the center for this hyperbola is (3, 3). Making both the h and the k three.
The distance between the center and either vertex is 'a'. This makes 'a' 2. The distance between the center and either focus is 'c'. This makes 'c' 4.
Since c^2 - a^2 = b^2, b^2 is 4^2 - 2^2 or 12.
Now just replace h, k, a^2 and b^2, giving:
(X - 3)^2/4 - (y - 3)^2/12 = 1