What is the coordinate of the vertex?

(6,-20)

Explanation:
The equation f(x) = -(x-6)^2 - 20 is the same as y = -1(x-6)^2 + (-20)
It is in the form y = a(x-h)^2 + k
The vertex is (h,k) 
In this case, h = 6 and k = -20
So that's why the vertex is (6,-20)