Given curves are

y^{2}= 2x ........(i)

and the line x - y = 4......(ii)

Obviously, curve (i) is right handed parabola having vertex at (0, 0) and axis along +ve direction of x-axis while curve (ii) is a straight line.

For intersection point of curve (i) and (ii)

Intersection points are (2, - 2), (8, 4). Therefore. required area = Area of shaded region