1. **State the problem:** Solve the system of equations: $$2x - 3y = -4$$ $$-6x + 9y = 12$$ 2. **Analyze the system:** Notice the second equation is a multiple of the first: Multiply the first equation by 3: $$3(2x - 3y) = 3(-4)$$ $$6x - 9y = -12$$ 3. **Compare with the second equation:** The second equation is: $$-6x + 9y = 12$$ 4. **Rewrite the second equation:** Multiply both sides by -1 to compare: $$-1(-6x + 9y) = -1(12)$$ $$6x - 9y = -12$$ 5. **Conclusion:** Both equations simplify to the same equation: $$6x - 9y = -12$$ This means the two equations represent the same line. 6. **Answer:** Since both equations represent the same line, the system has infinitely many solutions. **Final answer:** Infinite Solutions