Part A:
1 m = 39.4 in
In the solution provided meters (m) appears both at the numerator and the denominator. Because of this similarity, one can cancel out the other.
This is just to establish that if 1m is equivalent to 39.4in, then 1.5m should be a multiple of it to convert to inches
Similarly in part B:
1L = 1.06 quarts
To change 186 quarts to liters:
186qt x 1L/1.06qt
Quarts appears on both the numerator and denominator, which makes them cancel out since they are basically the same unit