The equation of a circle is (x+9)2+(y+6)2=225 .
what is the center of the circle?

The equation above is in center-radius form. In which, (x-h)² + (y-k)² = r².
the center of the circle is at point (h,k). 

applying it to the equation (x+9)² + (y+6)² = 225;

(x-h) = (x+9)
x - x - h = 9
-h = 9
h = -9

(y-k) = (y+6)
y - y - k = 6
-k = 6
k = -6

The center of the circle is at point (-9,-6)