1. **State the problem:** Verify if the expression $$\frac{2x^{2}y^{4} \cdot 4x^{2}y^{4} \cdot 3x}{3x^{-3} y^{2}}$$ is simplified correctly. 2. **Write the original expression:** $$\frac{2x^{2}y^{4} \cdot 4x^{2}y^{4} \cdot 3x}{3x^{-3} y^{2}}$$ 3. **Multiply the numerator terms:** $$2 \times 4 \times 3 = 24$$ For the variables, add exponents of like bases: $$x^{2} \cdot x^{2} \cdot x^{1} = x^{2+2+1} = x^{5}$$ $$y^{4} \cdot y^{4} = y^{8}$$ So numerator becomes: $$24 x^{5} y^{8}$$ 4. **Rewrite the denominator:** $$3 x^{-3} y^{2}$$ 5. **Divide numerator by denominator:** $$\frac{24 x^{5} y^{8}}{3 x^{-3} y^{2}} = \frac{24}{3} \times x^{5 - (-3)} \times y^{8 - 2} = 8 x^{8} y^{6}$$ 6. **Check the user's final answer:** User wrote: $$8 x^{13} y^{4}$$ Our calculation shows: $$8 x^{8} y^{6}$$ 7. **Conclusion:** The user's answer is incorrect. The correct simplified form is: $$8 x^{8} y^{6}$$