Define a new function $ h(x) $ so that $ h(x)=g(f(x)) $. Then \begin{align*} h(x) &= g\left(\frac{1+x}{1-x}\right)=\frac{-2}{\frac{1+x}{1-x}+1}\\ &= \frac{-2}{\frac{1+x}{1-x}+\frac{1-x}{1-x}}=\frac{-2}{\frac{2}{1-x}}\\ &= \frac{-1}{\frac{1}{1-x}}=-(1-x)=x-1.\end{align*}Thus our desired value is equivalent to $ 8 $ compositions of the function $ h(x) $. For each composition we subtract $ 1 $ from the input value, so for $ 8 $ compositions we subtract a total of $ 8 $ from the input value, which is $ 12 $. So our answer is $ 12-8=\boxed{4} $.