Move the minus sign from the denominator to the front of the expression.

`-(8x^(-3)-y^(-1))/(2x^6 y^(-4))`

Cancel the common factor of `2` in `-(8x^(-3)-y^(-1))/(2x^6 y^(-4))` since

`-(8x^(-3)-y^(-1))/(2x^6 y^(-4)) = ((-4y^3 * 2))/((x^9 * 2))`

Remove the common factors that were cancelled out.

`-(4y^3)/(x^9)`

Cancel the common factor of `x^-3` in `-(4y^3)/(x^9)` since

`-(4y^3)/(x^9) = ((-4y^3 * x^-3))/((x^9 * x^-3))`

`-(4y^3)/x^(9^9)`

Remove the common factors that were cancelled out.

`-(4y^3)/x^9`

Cancel the common factor of `y^-4` in `-(4y^3)/x^9` since `-(4y^3)/x^9 = ((-4y^3 * y^-4))/((x^9 * y^-4))`

`-(4y^(3^3))/(x^9)`

Reduce the expression `-(8x^(-3) y^(-1))/(2x^6 y^(-4))` by removing a factor of `2x^(-3) y^(-4)` from the numerator and denominator.

`-(4y^3)/x^9`

`(8x^(-3)y^(-1))/(-2x^6y^(-4))`

Divide both numerator and denominator by -2 and sum up the indices of like terms according to the law of indices,

`=-(4x^((-3-6))y^((-1+4)))` (since `p^m/p^n=p^((m-n))` )

`=-4x^(-9)y^3`

`=-4y^3/x^9`