1. **State the problem:** Solve the equation $6(x-4)=2x+4$ for $x$. 2. **Write down the formula and rules:** Use the distributive property to expand and then isolate $x$ by combining like terms and using inverse operations. 3. **Expand the left side:** $$6(x-4) = 6 \times x - 6 \times 4 = 6x - 24$$ 4. **Rewrite the equation:** $$6x - 24 = 2x + 4$$ 5. **Move all $x$ terms to one side and constants to the other:** $$6x - 2x = 4 + 24$$ 6. **Simplify both sides:** $$4x = 28$$ 7. **Divide both sides by 4 to solve for $x$:** $$x = \frac{28}{4}$$ 8. **Show cancellation:** $$x = \frac{\cancel{28}}{\cancel{4}} = 7$$ 9. **Final answer:** $$x = 7$$