1. **State the problem:** Simplify the complex fraction $$\frac{-1/2}{1/6}$$. 2. **Recall the rule for dividing fractions:** Dividing by a fraction is the same as multiplying by its reciprocal. So, $$\frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c}$$. 3. **Apply the rule:** $$\frac{-1}{2} \div \frac{1}{6} = \frac{-1}{2} \times \frac{6}{1}$$ 4. **Multiply the numerators and denominators:** $$= \frac{-1 \times 6}{2 \times 1} = \frac{-6}{2}$$ 5. **Simplify the fraction:** $$= \frac{\cancel{-6}^{\times 3}}{\cancel{2}^{\times 1}} = -3$$ 6. **Final answer:** $$-3$$