Vanessa has two bags that contain slips of paper. one bag has 4 slips of paper that are numbered 2, 3, 4, and 5. the other bag has 4 slips of paper that are numbered 3, 4, 5, and 6. vanessa chooses one slip of paper from each bag without looking. the random variable x is the product of the numbers on the slips of paper. what is p(12≤x≤15)? enter your answer

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

The answers are 20,30,80,180,960,890,1230,4560. on the first row