1. **State the problem:** Simplify the expression $-12 \div \frac{6}{5}$. 2. **Recall the rule:** Dividing by a fraction is the same as multiplying by its reciprocal. So, $a \div \frac{b}{c} = a \times \frac{c}{b}$. 3. **Apply the rule:** $$-12 \div \frac{6}{5} = -12 \times \frac{5}{6}$$ 4. **Multiply:** $$-12 \times \frac{5}{6} = \frac{-12 \times 5}{6} = \frac{-60}{6}$$ 5. **Simplify the fraction:** $$\frac{\cancel{-60}^{10} \times \cancel{6}^{1}}{\cancel{6}^{1}} = -10$$ 6. **Final answer:** $$\boxed{-10}$$