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The mistake which @CubeyThePenguin made in his post is H U G E.
I N E V E R saw people making such a H U G E mistake in such simple problem.
Below find my 2-lines correct solution.
The entire job is 8 men * 15 hours = 120 man-hours.
6 men will complete the job in = 20 hours. ANSWER
Solved (correctly).
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Direct proportion, which @CubeyThePenguin uses in his (or her) post, DOES NOT WORK for this problem.
For your safety, ignore his post.
Consider it as an example on how this problem should NEVER be solved.