1. **State the problem:** Simplify the expression $$\frac{(-6x^{2})^{3}}{(3x^{-4})^{2}}$$. 2. **Apply the power of a product rule:** For any numbers $a$ and $b$, and exponent $n$, we have $(ab)^n = a^n b^n$. 3. **Simplify numerator:** $$(-6x^{2})^{3} = (-6)^{3} (x^{2})^{3} = -216 x^{6}$$ 4. **Simplify denominator:** $$(3x^{-4})^{2} = 3^{2} (x^{-4})^{2} = 9 x^{-8}$$ 5. **Rewrite the fraction:** $$\frac{-216 x^{6}}{9 x^{-8}}$$ 6. **Divide coefficients and apply exponent rules:** $$\frac{-216}{9} \times \frac{x^{6}}{x^{-8}} = -24 \times x^{6 - (-8)} = -24 x^{14}$$ 7. **Final answer:** $$-24 x^{14}$$