This is a case where you can just enumerate all the possible outcomes and figure out how many fall within the criteria
If you pick the 2 from the first bag, you could get 2 x 3 = 6, 2 x 4 = 8, 2 x 5 = 10 and 2 x 6 = 12 Then you do it for 3, 4, and 5. The complete list is
6, 8, 10, 12 9. 12. 15. 18 12, 16, 20, 24 15, 20, 25, 30
That's 16 possible results. Then you just count the number of results that are between 12 and 15. Some results come up more than once, but since they come about by mutiplying different pairs on slips, they should all be counted
There's 1 result in range from the first row: 12 from muitplying 2 x 6 2 in the 2nd row: 12 from 3 x 4 and 15 from 3 x 5 1 in the 3rd row: 12 from 4 x 3 1 in the 4th row 15 from 5 x 3
So that's 5 out of 16. or 5/16