Dimensional analysis means to use the fundamental dimensions of the universe to determine the solution

In case you haven't been taught what those dimensions are: Length, Mass, Time, Absolute Temperature, and Charge.

The problem you mentioned uses speed, in this case a directionless average speed in units of miles per hour. That unit of speed is mi/hr and it corresponds to Length/Time in regards to dimensional analysis.

So you are given Length/Time and a Time and are tasked with finding Length. The equation is then:

Length = (Length/Time)*Time

you may be more familiar with this as d = r*t

using dimensional analysis your answer is Length = (48 mi/hr)*(7 hr) = 336 mi