1. Stating the problem: Simplify the expression $$\frac{4ab^3}{6a^2b}$$. 2. Write the expression as a fraction: $$\frac{4ab^3}{6a^2b}$$. 3. Simplify the coefficients: $$\frac{\cancel{4}}{\cancel{6}} = \frac{2}{3}$$. 4. Simplify the variables by subtracting exponents of like bases: - For $a$: $$\frac{a}{a^2} = a^{1-2} = a^{-1} = \frac{1}{a}$$. - For $b$: $$\frac{b^3}{b} = b^{3-1} = b^2$$. 5. Combine the simplified parts: $$\frac{2}{3} \times \frac{b^2}{a} = \frac{2b^2}{3a}$$. 6. Final answer: $$\frac{2b^2}{3a}$$.