Let $$f : R \to R$$ be a differentiable function having $$f(2) = 6, f'(2) = \left(\frac{1}{48}\right)$$. Then $$\lim_{x \to 2} \int_6^{f(x)} \frac{4t^3}{x - 2} dt$$ equals

A

$$24$$

B

$$36$$

C

$$12$$

D

$$18$$