1. **State the problem:** Solve the equation $$y + \frac{5}{6} = \frac{1}{6}$$ for $y$. 2. **Formula and rules:** To isolate $y$, subtract $\frac{5}{6}$ from both sides of the equation. 3. **Intermediate work:** $$y + \frac{5}{6} = \frac{1}{6}$$ Subtract $\frac{5}{6}$ from both sides: $$y + \frac{5}{6} - \frac{5}{6} = \frac{1}{6} - \frac{5}{6}$$ Simplify: $$y = \frac{1}{6} - \frac{5}{6}$$ $$y = \frac{1 - 5}{6}$$ $$y = \frac{-4}{6}$$ Simplify the fraction by dividing numerator and denominator by 2: $$y = \frac{\cancel{-4}^{2}}{\cancel{6}^{2}} = \frac{-2}{3}$$ 4. **Answer:** The solution is $y = -\frac{2}{3}$. This matches the second option in the multiple-choice list.