The most common and most likely answer to this crossword clue is the 6 plus 4 letter word PENCIL CASE
I've seen this crossword clue in The Times
P
E
N
C
I
L
C
A
S
E
Buddy explains!
The straight part
We know that "Box with drawers in" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case box with drawers in = pencil case.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.