The following table represents the sample space of rolling two number cubes.

1 2 3 4 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

How many favorable outcomes are there for the event "rolling exactly one even number"?

We just need to count the number of outcomes that have exactly one even number. The total number of outcomes is 36. We see that from the first row, the number of outcomes that qualify are 3: 1-2, 1-4, 1-6 (out of the 6 total outcomes). For the 2nd row, again there are 3: 2-1, 2-3, 2-5. It is obvious by now that for any row, whether the number is even or odd, there are 3 outcomes on that row that correspond to rolling exactly one even number. Hence, there are in total 6*3=18 favorable outcomes.