The most common and most likely answer to this crossword clue is the 4 plus 6 letter word FACE CLOTHS
F
A
C
E
C
L
O
T
H
S
Buddy explains!
The straight part
We know that "what to clean up with" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case what to clean up with = face cloths.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.