1. **State the problem:** Solve the equation $4(x+1)=2x+4$ for $x$. 2. **Write down the equation:** $$4(x+1)=2x+4$$ 3. **Distribute the 4 on the left side:** $$4 \times x + 4 \times 1 = 2x + 4$$ $$4x + 4 = 2x + 4$$ 4. **Subtract $2x$ from both sides to get all $x$ terms on one side:** $$4x + 4 - 2x = 2x + 4 - 2x$$ $$\cancel{4x} + 4 - \cancel{2x} = \cancel{2x} + 4 - \cancel{2x}$$ $$2x + 4 = 4$$ 5. **Subtract 4 from both sides to isolate the $x$ term:** $$2x + 4 - 4 = 4 - 4$$ $$2x + \cancel{4} - \cancel{4} = \cancel{4} - \cancel{4}$$ $$2x = 0$$ 6. **Divide both sides by 2 to solve for $x$:** $$\frac{2x}{2} = \frac{0}{2}$$ $$\cancel{2}x / \cancel{2} = 0$$ $$x = 0$$ **Final answer:** $$x = 0$$