JEE Math Practice Question

Let $$f$$ and $$g$$ be the twice differentiable functions on $$\mathbb{R}$$ such that $$f''(x)=g''(x)+6x$$ $$f'(1)=4g'(1)-3=9$$ $$f(2)=3g(2)=12$$. Then which of the following is NOT true?

1. A.$$g(-2)-f(-2)=20$$
2. B.There exists $$x_0\in(1,3/2)$$ such that $$f(x_0)=g(x_0)$$
3. C.$$|f'(x)-g'(x)| < 6\Rightarrow -1 < x < 1$$
4. D.If $$-1 < x < 2$$, then $$|f(x)-g(x)| < 8$$