1. **State the problem:** Solve the equation $$3y - \frac{1}{2} = \frac{2}{3}$$ for $y$. 2. **Isolate the term with $y$:** Add $\frac{1}{2}$ to both sides to get $$3y = \frac{2}{3} + \frac{1}{2}$$ 3. **Find a common denominator and add the fractions:** The common denominator of 3 and 2 is 6, so $$\frac{2}{3} = \frac{4}{6}, \quad \frac{1}{2} = \frac{3}{6}$$ Thus, $$3y = \frac{4}{6} + \frac{3}{6} = \frac{7}{6}$$ 4. **Solve for $y$ by dividing both sides by 3:** $$y = \frac{\frac{7}{6}}{3} = \frac{7}{6} \times \frac{1}{3} = \frac{7}{18}$$ 5. **Show the cancellation step explicitly:** $$y = \frac{\cancel{7}}{\cancel{6}} \times \frac{1}{3} = \frac{7}{18}$$ 6. **Final answer:** $$y = \frac{7}{18}$$ This means the value of $y$ that satisfies the equation is $\frac{7}{18}$.