Determine the result of the subtraction operation: $6 \frac{1}{4}-2 \frac{5}{6}$

Step 1 ：Convert the mixed numbers into improper fractions. The first number, $6 \frac{1}{4}$, becomes $\frac{25}{4}$ and the second number, $2 \frac{5}{6}$, becomes $\frac{17}{6}$.

Step 2 ：Subtract the two fractions: $\frac{25}{4} - \frac{17}{6} = \frac{41}{12}$.

Step 3 ：Final Answer: The result of the subtraction operation $6 \frac{1}{4}-2 \frac{5}{6}$ is \(\boxed{\frac{41}{12}}\).