The most common and most likely answer to this crossword clue is the 6 letter word BRAYED
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Buddy explains!

The straight part
We know that "laughed rudely" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case laughed rudely = brayed.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 BRAYED mean?
BRAYED verb- Of an animal (now chiefly of animals related to the ass or donkey, and the camel): to make its cry.
- (by extension) To make a harsh, discordant sound like a donkey's bray.
- To make or utter (a shout, sound, etc.) discordantly, loudly, or in a harsh and grating manner.
- To crush or pound, especially using a pestle and mortar.
- (by extension) To hit (someone or something).