When the quadratic function, f(x) is given as the equation of a
parabola in the form

f(x) = a(x-h)² + k

then the vertex of the parabola is (h,k)

Your function is

f(x) = -4(x+3)² + 6

So -h = +3 and h = -3 and k = 6, so the vertex is

(h,k) = (-3,6).

So you are correct.

Edwin