No, y is not equal to y^2! You can write y= sqrt(4x)= 2sqrt(x) and set that equal to 2x- 4. But it might be simpler to write x= y^2/4 so that y= 2(y^2/4)- 4= y^2/2- 4 and solve that quadratic equation.
I have to find the area of the area bound by y^2=4x and y=2x-4
I have to find the points of intersection. would I do this by solving 2x-4 = 4x or by 2x-4 = sqrt(4x) or both?