In the first case, you're splitting
packs among 8 people. If we look a this purely in terms of fifths, that's 3 whole packs (15/5) plus another 1/5, or 15/5 + 1/5 = 16/5 altogether. If we split 16 things among 8 people, each person gets 16 ÷ 8 = 2 things, so splitting 16/5 among 8 people gives each person 2/5 of a pack. Kevin and his friend's share is 2/5, so let's find Jane and her friends' so we can compare.
Jane is splitting
packs among 7 people. That's 2 whole packs (16/8) plus 5/8 of a pack, for a total of 16/8 + 5/8 = 21/8 of a pack. Splitting 21 things 7 ways leaves 21 ÷ 7 = 3 things per person, so splitting 21/8 7 ways gives each person 3/8 of a pack. We can now compare 3/8 with 2/5.
Notice that 2/5 is the same thing as 4/10. If we compare 3/8 and 4/10 to 1/2, we notice that both are one "piece" away - 3/8 is 1/8 less than 1/2, and 4/10 is 1/10 less than 1/2. 1/8 is bigger than 1/10, though, so 1/2 - 1/8 is smaller than 1/2 - 1/10, since we're taking a bigger amount away from it.
This means that Kevin & friends' share of 2/5 of a pack each is bigger than Jane & Co's share of 3/8 each.