If I may restate your question with (I hope) fully corrected grammar:
1) There are two boxes, A and B.
2) The size of A is twice that of B. -or- A is twice the size of B. -or- A is twice as big as B.
3) I have six apples to be placed into boxes.
4) Apples are allocated to boxes based on the box sizes.
5) Therefore, four apples go into box A and two into box B.
In statement 1, the verb must agree with the plurality of the noun, so you say "are", not "is", because you are talking about more than one box.
In statement 2, "twice larger than" is not standard phrasing. The options listed are all valid alternatives.
In statement 4, first of all we need the noun and the verb to match plurality again, so we say "are" because we still have more than one apple. Then, note that it is important to specify what item's sizes are being used as the basis of allocation. If you say "apples are allocated into boxes based on their sizes", I don't know if you mean the size of the apples, or the size of the boxes.