The maximum of f(x) is y = 3. This is the y coordinate of the vertex (6,3).
Note how y = -4(x-6)^2 + 3 is in the form y = a(x-h)^2 + k, which is vertex form. So we can see that the vertex is (h,k) = (6,3), since h = 6 and k = 3.
Note: This graph is an upside down parabola with (6,3) as the highest point.
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In contrast, the max of g(x) is y = 6. This is the y coordinate of the highest point on the curve. One such point is (pi/2, 6). There are infinitely max points because the up and down pattern goes on forever.
So g(x) has the larger max compared to f(x).