Simplify : \[ 8 \frac{1}{6}-2 \frac{1}{3} \]

Step 1 ：Convert the mixed numbers into improper fractions. The first number, \(8 \frac{1}{6}\), becomes \(\frac{49}{6}\) and the second number, \(2 \frac{1}{3}\), becomes \(\frac{7}{3}\).

Step 2 ：Subtract the two fractions: \(\frac{49}{6} - \frac{7}{3} = \frac{35}{6}\).

Step 3 ：Convert the improper fraction back into a mixed number to get the final answer: \(\boxed{5 \frac{5}{6}}\).