At the intersection point, the point is common to both curves. So the (x,y) of one is also the (x,y) of the other. Hence, solve the two equations simultaneously.

y^2 = x ---------(1)

y = x/4

4y = x -----------(2)

The x of (1) is also the x of (2), so,

y^2 = 4y

y^2 -4y = 0

y(y -4) = 0

y = 0 or 4

When y=0,

y^2 = x

0 = x

So, point (0,0)

When y = 4,

4^2 = x

x = 16

So, point (16,4)

Those two points are the intersections of the two curves (a parabola and a straight line).