The most common and most likely answer to this crossword clue is the 3 plus 3 letter word RED EYE
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Buddy explains!
The straight part
We know that "strong cup of coffee" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case strong cup of coffee = red eye.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 RED EYE mean?
RED EYE noun- The names of animals that have red eyes.
- Types of beverages.
- (travel) An overnight airplane flight.
- Redness of the conjunctiva; especially when caused by conjunctivitis (pink-eye).
- Redness in the eye(s) of someone in a colour photograph, as an unwanted consequence of light from a flash reflecting off blood vessels in the retina.
- (travel) Often followed by it: to travel on a red-eye.