The probability that only one shows a 2.
There are 36 different outputs (6x6) = 36
There are 6 combinations where the first cube shows a 2, these are 2,1;2,2;2,3;2,4;2,5; and 2.6
There are 6 combinations where the second cube shows a 2: 1,2;2,2;3,2;4,2;5,2; and 6,2.
Of those one combination on each set shows two 2.
Then the number of combinations with only one 2 are 6 - 1 + 6 -1 = 10
Now the probabilit is 10 out of 36 = 10 / 36 = 5 / 18