1. **State the problem:** Solve the equation $$2(2x - 8) = 3(4 - x)$$. 2. **Use the distributive property:** Multiply each term inside the parentheses by the factor outside. $$2 \times 2x - 2 \times 8 = 3 \times 4 - 3 \times x$$ which simplifies to $$4x - 16 = 12 - 3x$$. 3. **Collect like terms:** Add $3x$ to both sides to get all $x$ terms on one side. $$4x + 3x - 16 = 12 - 3x + 3x$$ which simplifies to $$7x - 16 = 12$$. 4. **Isolate the variable term:** Add $16$ to both sides. $$7x - 16 + 16 = 12 + 16$$ which simplifies to $$7x = 28$$. 5. **Solve for $x$:** Divide both sides by $7$. $$x = \frac{28}{7} = 4$$. **Final answer:** $$x = 4$$.