If f(x)=¼x2, f(x+3)=¼(x+3)2. f(x+3) is f(x) shifted 3 units to the left, so the vertex of f(x) is shifted from (0,0) to (-3,0).
When x=4 on f(x+3), y=f(x+3)=f(7)=49/4=12.25. So on f(x) this point was (7,12.25).
When x=4 on f(x), y=16/4=4 making the point (4,4) on f(x). Its image on f(x+3) would be (1,4) on f(x+3) because when x+3=4, x=1, so f(x+3)=f(4)=4.
It's much clearer if you draw the graphs of the two functions and compare them.
f(x) is shown in red and f(x+3) in blue. The green vertical is x=4.