1. **State the problem:** Solve the equation $$\frac{2x+4}{3} = 6$$ for $x$. 2. **Formula and rules:** To solve for $x$ in a fraction equation, multiply both sides by the denominator to eliminate the fraction. 3. **Multiply both sides by 3:** $$\cancel{3} \times \frac{2x+4}{\cancel{3}} = 6 \times 3$$ which simplifies to $$2x + 4 = 18$$ 4. **Isolate $x$:** Subtract 4 from both sides: $$2x + 4 - 4 = 18 - 4$$ $$2x = 14$$ 5. **Divide both sides by 2:** $$\frac{2x}{\cancel{2}} = \frac{14}{\cancel{2}}$$ $$x = 7$$ 6. **Final answer:** $x = 7$. This means the value of $x$ that satisfies the equation is 7.