1. **State the problem:** Simplify the expression $\frac{6}{-\sqrt{3}}$. 2. **Formula and rules:** To simplify a fraction with a square root in the denominator, multiply numerator and denominator by the conjugate or the same root to rationalize the denominator. 3. **Apply rationalization:** Multiply numerator and denominator by $\sqrt{3}$: $$\frac{6}{-\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{6\sqrt{3}}{-\sqrt{3}\sqrt{3}}$$ 4. **Simplify denominator:** Since $\sqrt{3}\sqrt{3} = 3$, we have: $$\frac{6\sqrt{3}}{-3}$$ 5. **Simplify fraction:** Divide numerator and denominator by 3: $$\frac{\cancel{6}\sqrt{3}}{-\cancel{3}} = \frac{2\sqrt{3}}{-1}$$ 6. **Final simplification:** $$-2\sqrt{3}$$ **Answer:** $-2\sqrt{3}$