1. **State the problem:** Simplify the expression $$\frac{5}{6}b + 5 - \frac{2}{3}b - 2$$ and express it in the form $$\frac{1}{6}b + [?]$$ where [?] is a number to find. 2. **Combine like terms:** Group the terms with $b$ and the constant terms separately: $$\left(\frac{5}{6}b - \frac{2}{3}b\right) + (5 - 2)$$ 3. **Find a common denominator for the $b$ terms:** The denominator 6 and 3 have a common denominator 6. Rewrite $$\frac{2}{3}b = \frac{4}{6}b$$. 4. **Subtract the $b$ terms:** $$\frac{5}{6}b - \frac{4}{6}b = \frac{5 - 4}{6}b = \frac{1}{6}b$$ 5. **Simplify the constants:** $$5 - 2 = 3$$ 6. **Write the simplified expression:** $$\frac{1}{6}b + 3$$ 7. **Identify the number in the green box:** The number that goes in the green box is **3**. **Final answer:** $$\frac{1}{6}b + 3$$