1. **State the problem:** Solve the equation $12 + 2d = 4d - 8$ for $d$. 2. **Write down the equation:** $$12 + 2d = 4d - 8$$ 3. **Isolate variable terms on one side:** Subtract $2d$ from both sides: $$12 + \cancel{2d} - \cancel{2d} = 4d - 8 - 2d$$ which simplifies to $$12 = 2d - 8$$ 4. **Isolate the constant term:** Add $8$ to both sides: $$12 + 8 = 2d - 8 + 8$$ which simplifies to $$20 = 2d$$ 5. **Solve for $d$ by dividing both sides by 2:** $$\frac{20}{\cancel{2}} = \frac{2d}{\cancel{2}}$$ which simplifies to $$10 = d$$ **Final answer:** $$d = 10$$