1. **State the problem:** Simplify the expression $$\frac{4x^{2}y^{-3} \cdot x^{4}y^{4}}{3xy^{2}}$$. 2. **Recall the rules:** - When multiplying powers with the same base, add exponents: $$a^{m} \cdot a^{n} = a^{m+n}$$. - When dividing powers with the same base, subtract exponents: $$\frac{a^{m}}{a^{n}} = a^{m-n}$$. - Negative exponents mean reciprocal: $$a^{-m} = \frac{1}{a^{m}}$$. 3. **Multiply the numerator terms:** $$4x^{2}y^{-3} \cdot x^{4}y^{4} = 4x^{2+4}y^{-3+4} = 4x^{6}y^{1} = 4x^{6}y$$ 4. **Rewrite the expression:** $$\frac{4x^{6}y}{3xy^{2}}$$ 5. **Divide the powers with the same base:** $$\frac{4x^{6}y^{1}}{3x^{1}y^{2}} = \frac{4}{3} x^{6-1} y^{1-2} = \frac{4}{3} x^{5} y^{-1}$$ 6. **Rewrite negative exponent:** $$\frac{4}{3} x^{5} \cdot \frac{1}{y} = \frac{4x^{5}}{3y}$$ 7. **Final answer:** $$\boxed{\frac{4x^{5}}{3y}}$$ This corresponds to option B).