Let's try it with another set of units and see if you can transfer the idea.
10 s/hr into ? ms/min
(10 s/hr)(1000 ms/s)(1 hr/60 min) = 166.67 ms/min
Keep track of your units and convert one at a time. You start with 10 s/hr. We'll convert seconds, the numerator, first. We want ms in the numerator, there are 1000 ms in a s, so we multiply by the factor 1000 ms/s. Seconds cancel (s in the numerator initially, and dividing by s here), and we end up with ms in the numerator. Same general principle for hr into min.