1. **State the problem:** Calculate the difference between $\frac{9}{1/3}$ minus $4 \frac{5}{6}$. 2. **Rewrite the mixed number:** $4 \frac{5}{6} = \frac{4 \times 6 + 5}{6} = \frac{24 + 5}{6} = \frac{29}{6}$. 3. **Simplify the first term:** $\frac{9}{1/3} = 9 \div \frac{1}{3} = 9 \times 3 = 27$. 4. **Set up the subtraction:** $27 - \frac{29}{6}$. 5. **Convert 27 to a fraction with denominator 6:** $27 = \frac{27 \times 6}{6} = \frac{162}{6}$. 6. **Subtract the fractions:** $$\frac{162}{6} - \frac{29}{6} = \frac{162 - 29}{6} = \frac{133}{6}.$$ 7. **Convert the improper fraction to a mixed number:** $\frac{133}{6} = 22 \frac{1}{6}$. **Final answer:** $22 \frac{1}{6}$