I will assume that the two equations are
1) y = -x^2 +2x + 4 and 2) x +y = 4
subtract 2 from 1 and you get
y -x - y = -x^2 + 2x + 4 - 4
-x = -x^2 +2x
x^2 -x -2x = 0
x^2 - 3x = 0
x(x-3)=0
x=0 and x - 3 =0
x=0 and x = 3
Then y = 4 - x
y = 4 - 0 and y = 4 -3
y = 4 and y =1
Solutions:
Points (0,4) and (3,1)