The probability of rolling two dice at the same time and getting a 4 with either die or the sum of the dice is 6

Suppose that the first die we roll comes up as a 1. The other die roll could be a 1, 2, 3, 4, 5, or 6. Now suppose that the first die is a 2. The other die roll again could be a 1, 2, 3, 4, 5, or 6. We have already found 12 potential outcomes, and have yet to exhaust all of the possibilities of the first die. But with a second dice, there will be 24 different possibilities.

Step-by-step explanation:

   1     2        34   5     6

1(1, 1)   (1, 2)   (1, 3)   (1, 4)  (1, 5)   (1, 6)

2(2, 1)   (2, 2)  (2, 3)  (2, 4)(2, 5)  (2, 6)

3(3, 1)   (3, 2)  (3, 3)  (3, 4)  (3, 5)  (3, 6)

4(4, 1)   (4, 2)  (4, 3)  (4, 4)  (4, 5)  (4, 6)

5(5, 1)   (5, 2)  (5, 3)  (5, 4)  (5, 5)  (5, 6)

6(6, 1)   (6, 2)  (6, 3)  (6, 4)  (6, 5)  (6, 6)