For this type of function we have to evaluate doing the inner function first, in this case g(11).

g(x) = √(x-2)

When x = 11, g(11) is √(11-2) = √9 = 3

So g(11) = 3

Now we evaluate the function f(g(11)), knowing that g(11) is 3

f(3) = 3^{2} - 6(3) + 3

f(3) = 9-18+3 = -6

So f(g(11)) = -6