$1 \frac{1}{5} \cdot 8 \frac{2}{4}=$

Step 1 ：\(1 \frac{1}{5} = \frac{6}{5}\)

Step 2 ：\(8 \frac{2}{4} = \frac{34}{4}\)

Step 3 ：\(\frac{6}{5} \cdot \frac{34}{4} = \frac{204}{20}\)

Step 4 ：\(\frac{204}{20} = \frac{51}{5}\)

Step 5 ：\(\frac{51}{5} = 10 \frac{1}{5}\)

Step 6 ：\(\boxed{10 \frac{1}{5}}\)