Ok well first of all let's calculate how many cartons there are of each size:
There are 264 cartons in total and 1/6 of these are small, 2/3 are medium and the rest are large, thus:
Number of small cartons = (1/6)*264 = 44
Number of medium cartons = (2/3)*264 = 176
Number of large cartons = 264 - (44 + 176)
= 264 - 220
= 44
Now we can calculate how many eggs are needed to fill each type of carton:
Each small carton holds 8 eggs, thus the number of eggs needed equals:
8*44 = 352 eggs
Each medium carton holds 12 eggs, thus the number of eggs needed equals:
12*176 = 2112 eggs
Each large carton holds 18 eggs, thus the number of eggs needed equals:
18*44 = 792 eggs
Thus the total number of eggs needed = 352 + 2112 + 792 = 3256