1. **State the problem:** Simplify the expression $$\frac{8}{9} - \frac{4}{5} + \frac{1}{6}$$. 2. **Find a common denominator:** The denominators are 9, 5, and 6. The least common multiple (LCM) of 9, 5, and 6 is 90. 3. **Rewrite each fraction with denominator 90:** $$\frac{8}{9} = \frac{8 \times 10}{9 \times 10} = \frac{80}{90}$$ $$\frac{4}{5} = \frac{4 \times 18}{5 \times 18} = \frac{72}{90}$$ $$\frac{1}{6} = \frac{1 \times 15}{6 \times 15} = \frac{15}{90}$$ 4. **Perform the operations:** $$\frac{80}{90} - \frac{72}{90} + \frac{15}{90} = \frac{80 - 72 + 15}{90} = \frac{23}{90}$$ 5. **Simplify the fraction if possible:** 23 is a prime number and does not divide 90, so the fraction is already in simplest form. **Final answer:** $$\frac{23}{90}$$