(a+b)^3=a^3+3a^2b+3ab^2+b^3. So if a=3x-2y and b=-4z we get:
(3x-2y)^3-12z(3x-2y)^2+48z^2(3x-2y)-64z^3.
(3x-2y)^3=27x^3-54x^2y+36xy^2-8y^3 and (3x-2y)^2=9x^2-12xy+4y^2.
Therefore:
(3x-2y-4z)^3=27x^3-54x^2y+36xy^2-8y^3 - 108x^2z+144xyz-48y^2z + 144xz^2-96yz^2-64z^3.