The question you opened
Six printers, six posters, six minutes
Six printers take 6 minutes to print 6 posters.
How long do 30 printers need for 30 posters?
6 minutes
Each printer spends 6 minutes on one poster. Adding printers and posters in step leaves the clock exactly where it was.
Six printers take 6 minutes to produce 6 posters. Thirty printers take 6 minutes to produce 30 posters. The number that refuses to move is the time. The wrong answer of 30 minutes comes from a reasonable looking instinct. Two of the three numbers went up fivefold, so surely the third does too. The instinct fails because the three numbers are not playing equal roles. Printers and posters are quantities. Minutes is a duration, and duration depends on the rate at which one printer works.
So find that rate. Six printers make six posters in six minutes, which means each printer made one poster in that time. One printer, one poster, six minutes. That is the fact the question is built on, and everything else follows from it. Now scale. Thirty printers working side by side each finish their own poster in six minutes, so thirty posters appear after six minutes. Give them 300 printers and 300 posters and the answer is still six minutes.
The printers are working in parallel, so adding more of them adds capacity while the speed of each one stays put. Change one number and the question becomes interesting again. Six printers making 30 posters would take 30 minutes, because now each printer has five posters to get through. Thirty printers making 6 posters take 6 minutes as well, since 24 of them stand idle. The general handle is to reduce everything to one worker and one job.
Ask how long a single unit takes to do a single task, then multiply by how many tasks each unit has to do. Machines, painters, taps filling a bath, servers handling requests: same shape every time. This is one of the classic questions used to catch fast answers, and it catches people who are fast at arithmetic more often than people who are slow, because the fast answer arrives before the roles of the three numbers have been checked.
Technique: Find the rate for one worker