(-3x^-4y^-2)^-1 / (x^4y^4z^4) ^-4
a negative exponent changes to positive when it's swapped from top to bottom
That is,
x^-4 = 1/x^4
1/x^-4 = x^4
and, raising powers to powers multiplies them.
So, your fraction can be written as
(x^4y^4z^4)^4 / (-3x^-4y^-2)
= x^16y^16z^16 / (-3/(x^4y^2))
= (x^16y^16z^16)(x^4y^2) / -3
= -1/3 x^20 y^18 z^16