1. **State the problem:** Solve the inequality $$6(2x+1) - 8 > 5(1+2x) - 9$$. 2. **Apply the distributive property:** $$6 \times 2x + 6 \times 1 - 8 > 5 \times 1 + 5 \times 2x - 9$$ which simplifies to $$12x + 6 - 8 > 5 + 10x - 9$$. 3. **Simplify both sides:** $$12x - 2 > 10x - 4$$. 4. **Isolate variable terms on one side:** Subtract $10x$ from both sides: $$12x - 10x - 2 > -4$$ which gives $$2x - 2 > -4$$. 5. **Isolate $x$:** Add 2 to both sides: $$2x > -4 + 2$$ $$2x > -2$$ 6. **Divide both sides by 2:** $$x > \frac{-2}{2}$$ $$x > -1$$. **Final answer:** $$\boxed{x > -1}$$