The most common and most likely answer to this crossword clue is the 5 plus 3 plus 6 letter word WHATS THE DAMAGE
I've seen this crossword clue in The Daily Telegraph
W
H
A
T
S
T
H
E
D
A
M
A
G
E
More clues leading to the result WHATS THE DAMAGE
Buddy explains!
The straight part
We know that "How much do I owe you" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case how much do i owe you = whats the damage.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.