1. **State the problem:** Solve the equation $$\frac{6d}{2d - 1} = 2d$$. 2. **Use the formula and rules:** To solve for $d$, multiply both sides by the denominator $2d - 1$ to eliminate the fraction, but remember $2d - 1 \neq 0$ to avoid division by zero. 3. Multiply both sides: $$\frac{6d}{2d - 1} \times (2d - 1) = 2d \times (2d - 1)$$ which simplifies to $$6d = 2d(2d - 1)$$ 4. Expand the right side: $$6d = 4d^2 - 2d$$ 5. Bring all terms to one side: $$0 = 4d^2 - 2d - 6d$$ which simplifies to $$0 = 4d^2 - 8d$$ 6. Factor out the common factor $4d$: $$0 = 4d(d - 2)$$ 7. Set each factor equal to zero: $$4d = 0 \implies d = 0$$ $$d - 2 = 0 \implies d = 2$$ 8. Check for restrictions: The denominator $2d - 1 \neq 0$ implies $$2d - 1 \neq 0 \implies d \neq \frac{1}{2}$$ 9. Both $d=0$ and $d=2$ do not violate the restriction, so both are valid solutions. **Final answer:** $$d = 0 \text{ or } d = 2$$