The most common and most likely answer to this crossword clue is the 6 letter word OBITER
O
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Buddy explains!
The straight part
We know that "by the way" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case by the way = obiter.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.
What does OBITER mean?
OBITER noun- An obiter dictum; a statement from the bench commenting on a point of law which is not necessary for the judgment at hand and therefore has no judicial weight, as opposed to ratio decidendi.
- Incidentally; in passing.