1. **State the problem:** Solve for $r$ in the equation $$\frac{r - 9}{3} = 3.$$\n\n2. **Formula and rules:** To solve for $r$, we want to isolate $r$ on one side. Since $r - 9$ is divided by 3, we can multiply both sides by 3 to cancel the denominator.\n\n3. **Multiply both sides by 3:**\n$$3 \times \frac{r - 9}{3} = 3 \times 3$$\nUsing the cancellation rule, we get:\n$$\cancel{3} \times \frac{r - 9}{\cancel{3}} = 9$$\nwhich simplifies to\n$$r - 9 = 9.$$\n\n4. **Add 9 to both sides to isolate $r$:**\n$$r - 9 + 9 = 9 + 9$$\n$$r = 18.$$\n\n5. **Final answer:**\n$$r = 18.$$