Let me break this up.
Note: (f o g)(2) = f(g(2)).
Note: g(2) = (2, 2) means when x is 2 y is 2.
In other words, g(2) is 2.
We know that f(g(2)) = f(2).
You can see that f(2) = -3. This is given in the point (2, -3).
So, f(g(2)) = -3.
Done.
