1. **State the problem:** Simplify the expression $$\left( \frac{2x^2 y^3}{x^3 y} \right)^3$$. 2. **Apply the quotient rule for exponents:** When dividing like bases, subtract the exponents: $$\frac{x^a}{x^b} = x^{a-b}$$. 3. **Simplify inside the parentheses:** $$\frac{2x^2 y^3}{x^3 y} = 2 \cdot x^{2-3} \cdot y^{3-1} = 2x^{-1} y^{2} = \frac{2y^2}{x}$$. 4. **Raise the simplified expression to the power 3:** $$\left( \frac{2y^2}{x} \right)^3 = \frac{2^3 (y^2)^3}{x^3} = \frac{8 y^{6}}{x^3}$$. 5. **Final answer:** $$\frac{8 y^{6}}{x^{3}}$$ which corresponds to option **b**.