Divide. \[ \left(24 x^{6} y^{6}-33 x^{6} y^{3}\right) \div\left(-4 x^{4} y^{5}\right) \] Simplify your answer as much as possible.

To simplify the expression \[ \left(24 x^{6} y^{6}-33 x^{6} y^{3}\right) \div\left(-4 x^{4} y^{5}\right), \] we can start by factoring the numerator: \[ 24 x^6 y^6 - 33 x^6 y^3 = x^6 (24 y^6 - 33 y^3). \] Next, we can factor out \( 3y^3 \) from \( 24 y^6 - 33 y^3 \): \[ 24 y^6 - 33 y^3 = 3y^3(8y^3 - 11). \] Thus, the numerator can be rewritten as: \[ x^6 (3y^3 (8y^3 - 11)) = 3x^6 y^3 (8y^3 - 11). \] Now substituting this back into the division gives us: \[ \frac{3x^6 y^3 (8y^3 - 11)}{-4 x^4 y^5}. \] We can simplify by dividing both the numerator and the denominator. We can cancel \( x^4 \) in the numerator with \( x^6 \): \[ \frac{3 x^{6-4} y^3 (8y^3 - 11)}{-4 y^5} = \frac{3 x^2 (8y^3 - 11)}{-4 y^{3-5}} = \frac{3 x^2 (8y^3 - 11)}{-4 y^{-2}}. \] To account for the negative exponent, we rewrite it as: \[ \frac{3 x^2 (8y^3 - 11) \cdot y^2}{-4} = -\frac{3 x^2 y^2 (8y^3 - 11)}{4}. \] This is a simplified expression of the division. Thus, \[ \boxed{-\frac{3 x^2 y^2 (8y^3 - 11)}{4}}. \]