My assumption is that the "more than 2" hint applied to the number of candies in each of the two bags
The answer is
Yveti and Xerni know that there mus be more than 2 candies in each bag
Yveti is told the product is 24 but needs to choose two possible answers (3,8) and (4,6)
Xerni is told the sum is 11 but needs to choose three possible answers (3,8) (4,7) and (5,6)
Once Yveti says "I cant figure it out then the answer becomes clear.
If the answer was (4,7) whose product is 28, Yveti would immediately know the sum was 11 (4,7) since factors (2,14) would leave only 2 candies in one bag.
If the answer was (5,6) whose product is 30, Yveti would know the sum was either 13 (3,10) or 11 (5,6) since 17 (2,15) would leave only 2 candies in one bag. Two options remain
If the answer was (3,8) whose product is 24 the Yveti would know the sum was 10 (6,4) or 11 (3, 8) since 14 (2,12) would leave only 2 candies in one bag. Two options remain
If the sum was 10 (7,3) or (6,4) than Xerni would know the know that if Yveti was told the product was 21 (7,3) then Yveti could answer right away because there is no other solution.
Since Yveti did not answer right away the answer cannot have sum of 10. Since the sum is 11 and (5,6) and (7,4) already are excluded (for the reasons above) the answer by process of elimination is
product 24, sum 11
neither can answer on their own but after
Xerni after a long time, complains, "I can't figure it out!"
Yveti replies, "Me too!"
then Xerni and Yveti could