We haveg''(x) = 4, g'(0) = 0 and g(0) = 4

Start with the function g''(x) = 4 and find its primitive functiong''(x) = 4 => g'(x) = 4x+C

Since g'(0) = 4 we haveg'(x) = 4x+C => 4*0+C = 0 <=> C = 0

Finding the primitive function of f'(x) gives usg'(x) = 4x => g(x) = 2x^2+D

Since g(0) = 4 we haveg(x) = 2x^2+D => 4 = 2*0^2+D <=> D = 4

Thus, g(x) = 2x^2+4