1. **State the problem:** We have three vertical parallel lines cut by two transversals, creating segments labeled 12 and 8 on the top line, and segments 3y and y + 5 on the middle and bottom lines respectively. We need to find the value of $y$. 2. **Use the property of parallel lines and transversals:** When parallel lines are cut by transversals, corresponding segments are proportional. So, the ratio of segments on the top line equals the ratio of segments on the other lines. 3. **Set up the proportion:** $$\frac{12}{8} = \frac{3y}{y+5}$$ 4. **Simplify the left side:** $$\frac{12}{8} = \frac{3}{2}$$ 5. **Write the equation:** $$\frac{3}{2} = \frac{3y}{y+5}$$ 6. **Cross multiply:** $$3(y+5) = 2(3y)$$ 7. **Expand both sides:** $$3y + 15 = 6y$$ 8. **Isolate $y$:** $$15 = 6y - 3y$$ $$15 = 3y$$ 9. **Divide both sides by 3:** $$\frac{15}{\cancel{3}} = \frac{3y}{\cancel{3}}$$ $$5 = y$$ 10. **Final answer:** $$\boxed{5}$$ This matches the value provided, confirming the solution.