Suppose, you are rolling two regular six-sided dice and two four-sided dice together. Let's say, the sum of the numbers appearing on the first two regular six-sided dice is 'A' and the sum of the numbers appearing on the two four-sided dice is 'B'. What is the probability that the product of A and B is 12?

Note: A regular six-sided die has 1, 2, 3, 4, 5 and 6 on its faces. A four-sided die has four faces with 1, 2, 3 and 4 written on them