1. **State the problem:** Calculate $\frac{3}{20}$ of $\left(4 \frac{1}{3} - 2 \frac{1}{5}\right)$. 2. **Convert mixed numbers to improper fractions:** $4 \frac{1}{3} = \frac{13}{3}$ and $2 \frac{1}{5} = \frac{11}{5}$. 3. **Rewrite the expression:** $\frac{3}{20} \times \left(\frac{13}{3} - \frac{11}{5}\right)$. 4. **Find common denominator and subtract inside the parentheses:** Common denominator of 3 and 5 is 15. $\frac{13}{3} = \frac{65}{15}$ and $\frac{11}{5} = \frac{33}{15}$. So, $\frac{65}{15} - \frac{33}{15} = \frac{32}{15}$. 5. **Multiply by $\frac{3}{20}$:** $\frac{3}{20} \times \frac{32}{15} = \frac{3 \times 32}{20 \times 15} = \frac{96}{300}$. 6. **Simplify the fraction:** $\frac{96}{300} = \frac{\cancel{96}^{32}}{\cancel{300}^{100}} = \frac{32}{100}$. 7. **Simplify further:** $\frac{32}{100} = \frac{\cancel{32}^{8}}{\cancel{100}^{25}} = \frac{8}{25}$. **Final answer:** $$\frac{3}{20} \times \left(4 \frac{1}{3} - 2 \frac{1}{5}\right) = \frac{8}{25}.$$