1. **State the problem:** We have a spinner divided into 12 equal sections numbered 1 through 12. We want to find the probability that the spinner lands on a number that is a multiple of both 2 and 3. 2. **Understand the problem:** A number that is a multiple of both 2 and 3 is a multiple of their least common multiple (LCM). The LCM of 2 and 3 is 6. 3. **Identify favorable outcomes:** The numbers between 1 and 12 that are multiples of 6 are 6 and 12. 4. **Calculate the probability:** Probability is given by the formula: $$\text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}$$ Here, the number of favorable outcomes is 2 (6 and 12), and the total number of outcomes is 12. 5. **Simplify the fraction:** $$\frac{2}{12} = \frac{\cancel{2}^1}{\cancel{12}^6} = \frac{1}{6}$$ 6. **Final answer:** The probability that the spinner lands on a number that is a multiple of both 2 and 3 is **$\frac{1}{6}$**.