1. **State the problem:** Multiply the mixed fractions $2 \frac{4}{5}$ and $2 \frac{1}{7}$. Simplify the result. 2. **Convert mixed fractions to improper fractions:** $$2 \frac{4}{5} = \frac{2 \times 5 + 4}{5} = \frac{10 + 4}{5} = \frac{14}{5}$$ $$2 \frac{1}{7} = \frac{2 \times 7 + 1}{7} = \frac{14 + 1}{7} = \frac{15}{7}$$ 3. **Multiply the improper fractions:** $$\frac{14}{5} \times \frac{15}{7} = \frac{14 \times 15}{5 \times 7} = \frac{210}{35}$$ 4. **Simplify the fraction:** $$\frac{210}{35} = \frac{\cancel{210}^{6 \times 35}}{\cancel{35}^{1 \times 35}} = \frac{6}{1} = 6$$ 5. **Final answer:** $$6$$ The product of $2 \frac{4}{5}$ and $2 \frac{1}{7}$ is $6$.