1. **State the problem:** Solve the equation $\frac{3}{7} = -\frac{9}{14}d$ for $d$. 2. **Formula and rules:** To solve for $d$, we want to isolate $d$ on one side of the equation. We can do this by multiplying both sides by the reciprocal of the coefficient of $d$. 3. **Isolate $d$:** Multiply both sides by $-\frac{14}{9}$: $$d = \frac{3}{7} \times -\frac{14}{9}$$ 4. **Simplify the multiplication:** $$d = -\frac{3 \times 14}{7 \times 9}$$ 5. **Simplify numerator and denominator:** $$d = -\frac{42}{63}$$ 6. **Reduce the fraction by dividing numerator and denominator by 21:** $$d = -\frac{2}{3}$$ **Final answer:** $$d = -\frac{2}{3}$$