1. **State the problem:** Multiply the mixed numbers $6 \frac{4}{5}$ and $2 \frac{3}{5}$. 2. **Convert mixed numbers to improper fractions:** $6 \frac{4}{5} = \frac{6 \times 5 + 4}{5} = \frac{30 + 4}{5} = \frac{34}{5}$ $2 \frac{3}{5} = \frac{2 \times 5 + 3}{5} = \frac{10 + 3}{5} = \frac{13}{5}$ 3. **Multiply the improper fractions:** $$\frac{34}{5} \times \frac{13}{5} = \frac{34 \times 13}{5 \times 5} = \frac{442}{25}$$ 4. **Simplify the fraction if possible:** $442$ and $25$ have no common factors other than 1, so the fraction is already in simplest form. 5. **Convert the improper fraction back to a mixed number:** Divide $442$ by $25$: $442 \div 25 = 17$ remainder $17$ So, $$\frac{442}{25} = 17 \frac{17}{25}$$ 6. **Final answer:** $$6 \frac{4}{5} \times 2 \frac{3}{5} = 17 \frac{17}{25}$$