1. **State the problem:** Solve the system of equations: $$3x - 2y = -8$$ $$-6x + 4y = 16$$ 2. **Analyze the system:** Notice the second equation is exactly $-2$ times the first equation: $$-2 \times (3x - 2y) = -2 \times (-8)$$ $$-6x + 4y = 16$$ 3. **Interpretation:** Since the second equation is a multiple of the first, both equations represent the same line. 4. **Conclusion:** The system has infinitely many solutions because the two equations are dependent and represent the same line. **Final answer:** The system has **infinite solutions**.