1. **State the problem:** Solve the system of inequalities $$-4a < 20$$ and $$-9 > a - 6$$. 2. **Solve the first inequality:** $$-4a < 20$$. Divide both sides by $$-4$$, remembering to reverse the inequality sign because we divide by a negative number: $$\cancel{-4}a > \frac{20}{\cancel{-4}}$$ which simplifies to: $$a > -5$$. 3. **Solve the second inequality:** $$-9 > a - 6$$. Add 6 to both sides: $$-9 + 6 > a - 6 + 6$$ which simplifies to: $$-3 > a$$ or equivalently: $$a < -3$$. 4. **Combine the solutions:** From the first inequality, $$a > -5$$. From the second inequality, $$a < -3$$. Therefore, the solution is: $$-5 < a < -3$$. This means $$a$$ is any number between $$-5$$ and $$-3$$, not including $$-5$$ and $$-3$$ themselves.