1. The problem is to simplify the expression $$\frac{2x^3}{3x^2} \times \frac{4x^3}{6x}$$ and find the simplified result. 2. Start by rewriting the expression: $$\frac{2x^3}{3x^2} \times \frac{4x^3}{6x}$$ 3. Multiply the numerators and denominators: $$\frac{2x^3 \times 4x^3}{3x^2 \times 6x} = \frac{8x^{3+3}}{18x^{2+1}} = \frac{8x^6}{18x^3}$$ 4. Simplify coefficients and powers of x: $$\frac{8}{18} = \frac{4}{9}, \quad \frac{x^6}{x^3} = x^{6-3} = x^3$$ 5. Therefore, the simplified expression is: $$\frac{4}{9} x^3$$ 6. Final answer: $$\boxed{\frac{4}{9}x^3}$$