1. **State the problem:** Simplify the expression $\frac{-3}{4} \div \frac{-6}{7}$. 2. **Recall the division rule for 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:** $$\frac{-3}{4} \div \frac{-6}{7} = \frac{-3}{4} \times \frac{7}{-6}.$$ 4. **Multiply the numerators and denominators:** $$\frac{-3 \times 7}{4 \times -6} = \frac{-21}{-24}.$$ 5. **Simplify the fraction:** Both numerator and denominator are negative, so the fraction is positive. $$\frac{-21}{-24} = \frac{21}{24}.$$ 6. **Reduce the fraction by dividing numerator and denominator by their greatest common divisor (3):** $$\frac{\cancel{21}^{7}}{\cancel{24}^{8}} = \frac{7}{8}.$$ 7. **Final answer:** $$\frac{-3}{4} \div \frac{-6}{7} = \frac{7}{8}.$$