1. **State the problem:** Solve the linear equation $2x + 6 = 12$ for $x$. 2. **Formula and rules:** To solve for $x$, isolate the variable by performing inverse operations. Subtract or add terms on both sides to simplify. 3. **Step 1:** Subtract 6 from both sides: $$2x + 6 - 6 = 12 - 6$$ which simplifies to $$2x = 6$$ 4. **Step 2:** Divide both sides by 2 to isolate $x$: $$\frac{2x}{2} = \frac{6}{2}$$ which simplifies to $$x = 3$$ 5. **Final answer:** $x = 3$. This means the value of $x$ that satisfies the equation is 3.