1. **State the problem:** Solve the two-step equation $$6x + 12 = 84$$ for $$x$$ where the solution is a positive integer. 2. **Formula and rules:** The general form of a two-step equation is $$ax + b = c$$. To solve for $$x$$, first isolate the term with $$x$$ by subtracting $$b$$ from both sides, then divide both sides by $$a$$. 3. **Step 1: Subtract 12 from both sides** $$6x + 12 - 12 = 84 - 12$$ $$6x = 72$$ 4. **Step 2: Divide both sides by 6** $$x = \frac{72}{6}$$ 5. **Simplify the fraction with cancellation:** $$x = \frac{\cancel{72}}{\cancel{6}} = 12$$ 6. **Final answer:** $$x = 12$$ The solution is a positive integer as required.