1. **State the problem:** Simplify the expression $$\frac{-12x^{-5}y}{(4x^3)^{-2}}$$. 2. **Recall the rule for negative exponents:** For any nonzero number $a$ and integer $n$, $$a^{-n} = \frac{1}{a^n}$$. 3. **Apply the negative exponent to the denominator:** $$(4x^3)^{-2} = \frac{1}{(4x^3)^2} = \frac{1}{4^2 x^{3 \times 2}} = \frac{1}{16x^6}$$. 4. **Rewrite the original expression using this:** $$\frac{-12x^{-5}y}{(4x^3)^{-2}} = -12x^{-5}y \times 16x^6$$. 5. **Multiply the constants and the powers of $x$:** $$-12 \times 16 = -192$$ $$x^{-5} \times x^6 = x^{-5+6} = x^1 = x$$. 6. **Combine all parts:** $$-192xy$$. **Final answer:** $$-192xy$$