Solve for \( y \). \( -2 y-4(-6 y-6)=-4-6(-3-y) \) One solution, and \( y= \) No solution Infinite number of solutions

1. **Start with the equation:** \[ -2y - 4(-6y - 6) = -4 - 6(-3 - y) \] 2. **Simplify both sides:** - **Left side:** \[ -2y - 4(-6y - 6) = -2y + 24y + 24 = 22y + 24 \] - **Right side:** \[ -4 - 6(-3 - y) = -4 + 18 + 6y = 14 + 6y \] 3. **Set the simplified expressions equal to each other:** \[ 22y + 24 = 14 + 6y \] 4. **Isolate \( y \):** - Subtract \(6y\) from both sides: \[ 22y - 6y + 24 = 14 \quad \Rightarrow \quad 16y + 24 = 14 \] - Subtract \(24\) from both sides: \[ 16y = 14 - 24 \quad \Rightarrow \quad 16y = -10 \] - Divide both sides by \(16\): \[ y = \frac{-10}{16} = -\frac{5}{8} \] 5. **Conclusion:** There is one solution, and \( y = -\frac{5}{8} \).