What is the answer

I think you dreamed this one up!

    (-2mn^2)^(-3)/4m^(-6)n^(4) = -1/(32 m^9 n^2)

$\frac{(-2mn^2)^3}{4m^{-6}n^4}$

$= \frac{-8m^3n^6(m^6)}{4n^4}$

$= -2m^9n^2$