Answer
$$\frac{a}{3b^{2}}$$
Work Step by Step
To simplify, first factor numerator and denominator:
$$\frac{4a^{2}b}{12ab^{3}}=\frac{4\times a\times a\times b}{3\times 4\times a\times b\times b^{2}}.$$
Cancel common factors $4$, $a$, and $b$:
$$\frac{a}{3b^{2}}.$$
