We can write $$(1 - x^{6})^{4}= 4C0(1)^4(x^6)^0-4C1(1)^3(x^6)^1+4C2(1)^2(x^6)^2-4C3(1)^1(x^6)^3+4C4(1)^0(x^6)^4$$ $$Rightarrow$$ $$(1 - x^{6})^{4}= (1-4x^6+6x^{12}-4x^{18}+x^{24})$$ Therefore, we can say $$(1 - x^{6})^{4}(1 - x)^{-4}=(1-4x^6+6x^{12}-4x^{18}+x^{24})*(1 - x)^{-4}$$
We have to find out coefficient of $$x^{12}$$, $$x^6$$, $$x^0$$ in $$(1 - x)^{-4}$$. We can use binomial expansion for negative coefficients. Therefore, coefficient of $$x^{12}$$ in $$(1 - x)^{-4}$$ $$Rightarrow$$ $$dfrac{(-4)*(-4-1)*(-4-2)* ... *(-4-11)}{12!}$$ $$Rightarrow$$ $$dfrac{15!}{12!*3!}$$
$$Rightarrow$$ $$dfrac{15*14*13}{3*2*1}$$
$$Rightarrow$$ $$455$$
Similarly, coefficient of $$x^6$$ in $$(1 - x)^{-4}$$ $$Rightarrow$$ $$dfrac{(-4)*(-4-1)*(-4-2)* ... *(-4-5)}{6!}$$
$$Rightarrow$$ $$dfrac{9!}{6!*3!}$$
$$Rightarrow$$ $$dfrac{7*8*9}{3*2*1}$$
$$Rightarrow$$ $$84$$
Coefficient of $$x^0$$ in $$(1 - x)^{-4}$$ is 1.  Therefore, we can say that the coefficient of $$x^{12}$$ in the expansion of $$(1 - x^{6})^{4}(1 - x)^{-4}$$ = 455+(-4*84)+(1*6) = 125. Hence, option C is the correct answer.