Step 1 :The problem is asking for the probability that the result of spinning the spinner is a number that is both a multiple of 6 and a multiple of 4. The numbers that are multiples of both 6 and 4 are the common multiples of 6 and 4.
Step 2 :To solve this problem, we need to find the common multiples of 6 and 4 that are between 1 and 12 (inclusive), and then divide the number of these common multiples by the total number of possible outcomes (which is 12, because there are 12 equal areas on the spinner).
Step 3 :The common multiples of 6 and 4 between 1 and 12 are \([12]\).
Step 4 :So, the probability is \(\frac{1}{12}\).
Step 5 :Final Answer: The probability that the result is a multiple of 6 and a multiple of 4 is \(\boxed{\frac{1}{12}}\).