If 6 machines run at the same constant rate, they can

6 machines can do a job in 8 hrs.
5 machines con do a job in ?

Now think, will 5 machines take more than 8 hrs, or less? Of course more than 8 hrs since fewer machines are working.

So number of hours 5 machines will take = \(8 * (\frac{6}{5})\)

Basically, you need hours so given hours term i.e. \(8 * \frac{6 machines}{5 machines}\) to get 9.6 hours.

We multiply by 6/5 to increase 8 since more hours are required.
It is actually a Variation question (Inverse Variation here) but it is just easier to think in terms of more/less.

Another e.g. 10 people make 5 chairs in a day. How many people do we need to make 12 chairs.
Simply multiply 10 (the number that you want to change) by 12/5 because you want to increase the number of people to make more chairs: \(10 * (\frac{12}{5}) = 24\) people

Yet another e.g. 10 people need 4 hours to complete a job. How many hours do 18 people need to complete the same job?
\(4 * (\frac{10}{18})\) = 2.2 hrs
If there are more people, they will need fewer hours so multiply by 10/18 (not 18/10).