1. **Problem:** Simplify the polynomial expression $6x^3 - 9x + 12$. 2. **Formula and rules:** This is a polynomial expression. Simplification involves combining like terms if any, but here terms have different powers of $x$, so no further simplification is possible. 3. **Intermediate work:** The expression is already simplified: $$6x^3 - 9x + 12$$ 4. **Explanation:** Since the terms have different powers of $x$ (cubic, linear, and constant), they cannot be combined further. 5. **Final answer:** $$6x^3 - 9x + 12$$