6. $7 \frac{5}{8} \times 9 \frac{3}{5}$

Step 1 ：Convert the mixed numbers into improper fractions. The first mixed number, \(7 \frac{5}{8}\), becomes \(\frac{61}{8}\) and the second mixed number, \(9 \frac{3}{5}\), becomes \(\frac{48}{5}\).

Step 2 ：Next, multiply the two fractions together. This gives us \(\frac{366}{40}\).

Step 3 ：Simplify the fraction by finding the greatest common divisor (gcd) of the numerator and the denominator. The gcd of 366 and 40 is 8, so we divide both the numerator and the denominator by 8 to get \(\frac{366}{8}\) and \(\frac{40}{8}\), which simplifies to \(\frac{45.75}{5}\).

Step 4 ：Convert the improper fraction back to a mixed number. The whole number part is 73 and the fractional part is \(\frac{1}{5}\).

Step 5 ：\(\boxed{73 \frac{1}{5}}\) is the final answer.