2. \( \frac{12 a^{2} b^{3}}{3 a b} \)

To simplify the expression \( \frac{12 a^{2} b^{3}}{3 a b} \), we start by dividing both the coefficients and the variables. The coefficient simplifies as follows: \( \frac{12}{3} = 4 \). Now for the variables, we have \( \frac{a^2}{a} = a^{2-1} = a \) and \( \frac{b^{3}}{b} = b^{3-1} = b^{2} \). Combining these results gives us \( 4ab^{2} \). So, the simplified expression is \( 4ab^{2} \). Now let's keep it fun! Simplifying algebraic expressions is like solving a puzzle where you get to combine like terms, slice numbers, and create something new. Every term you eliminate is like trimming the fat to find the lean, mean mathematical machine that is the simplified form!