1. **Stating the problem:** Simplify the expression $$\frac{12p^4 \times 3q^{-3}}{\frac{18p}{q^5}}$$. 2. **Write the expression clearly:** $$\frac{12p^4 \times 3q^{-3}}{\frac{18p}{q^5}} = \frac{12p^4 \times 3q^{-3}}{1} \times \frac{q^5}{18p}$$ 3. **Multiply the numerators and denominators:** $$= \frac{12 \times 3 \times p^4 \times q^{-3} \times q^5}{18 \times p}$$ 4. **Simplify constants:** $$12 \times 3 = 36$$ 5. **Simplify powers of $p$:** $$\frac{p^4}{p} = p^{4-1} = p^3$$ 6. **Simplify powers of $q$:** $$q^{-3} \times q^5 = q^{-3+5} = q^2$$ 7. **Put it all together:** $$\frac{36 p^3 q^2}{18}$$ 8. **Simplify the fraction:** $$\frac{36}{18} = 2$$ 9. **Final simplified expression:** $$2 p^3 q^2$$ **Answer:** Option B. 2p^3 q^2