Yep...confusing !!!
Note that g(x) = 3 can be considered as the line y = 3
So....note that any x value on this line will have the associated y value of 3
So.....for example.....the points (-1, 3) (0, 3) (1, 3) ( 2, 3) (3, 3) etc. are all on the line
So g(2) is really the point (2, 3)
So g(2) = 3
Hope that makes some sense !!!