To multiply the two fractions, we will first write the expression:
\[ \frac{(a - b)^2}{3} \times \frac{24}{2(a - b)} \]
Now we can multiply the two fractions together:
\[ \frac{(a - b)^2 \cdot 24}{3 \cdot 2(a - b)} \]
This simplifies to:
\[ \frac{24(a - b)^2}{6(a - b)} \]
Next, we can simplify the fraction. Notice that \((a - b)\) in the numerator and the denominator cancels out (as long as \(a \neq b\)):
\[ \frac{24(a - b)}{6} \]
Now, simplify the coefficients:
\[ \frac{24}{6} = 4 \]
So we have:
\[ 4(a - b) \]
Therefore, the final simplified answer is:
\[ 4(a - b) \]