I tried by solving inequality of numerator and denominator

*Numerator*:

$(1+a)(1+c)(1+c) \leq \frac{(3 + a + b + c)}{3} = \frac{(3 + 1)}{3} = \frac{4}{3}$

*Denominator*:

$(1-a)(1-c)(1-c) \leq \frac{3 - (a + b + c)}{3} = \frac{(3 - 1)}{3} = \frac{2}{3}$

By combining the 2 equations

$\frac{Numerator}{Denominator} \leq \frac{4/3}{2/3} = 2$

But that's not the answer (I know I found max value). Can anyone help me? Is the method I am following can be used in other types of question? Solving Numerator and denominator inequality and than dividing both inequatlity....

ANSWER: 8