1. **State the problem:** We need to find how many solutions the equation $$2(x - 4) = 4 - 2x$$ has. 2. **Write the equation:** $$2(x - 4) = 4 - 2x$$ 3. **Expand the left side:** $$2x - 8 = 4 - 2x$$ 4. **Add $$2x$$ to both sides:** $$2x + 2x - 8 = 4 - \cancel{2x} + \cancel{2x}$$ This simplifies to $$4x - 8 = 4$$ 5. **Add 8 to both sides:** $$4x - 8 + 8 = 4 + 8$$ Simplifies to $$4x = 12$$ 6. **Divide both sides by 4:** $$\frac{4x}{\cancel{4}} = \frac{12}{\cancel{4}}$$ Simplifies to $$x = 3$$ 7. **Interpretation:** Since we found a single value $$x=3$$ that satisfies the equation, there is exactly one solution. **Final answer:** B. One