8 dozen bagels means he has 8 x 12 = 96 bagels.
If each plate holds 14 bagels, then (96 bagels) / (14 bagels / plate) = 6.857 plates.
You can't have 0.857 of a plate, so you have to round up to 7 plates.
If there are 7 plates, and 6 of them are full, then the first 6 plates have: (6 plates) x (14 bagels / plate) = 84 bagels.
Remember Corsetti had 96 bagels total, so (96 bagels) - (84 bagels) gives us the number of bagels on the last plate, which is 12.
Since each plate can hold 14, and we only have 12 on the last plate, it would take two more bagels to fill the final plate with bagels.