It doesn't matter which order you carry out multiplication or division operations in (this is a general mathematical rule).
I prefer to state it as divide by 144 first as I find it a bit more logical. 144 is 12 squared. The quarter-girth measurement is made in inches. Squaring it gives an area in square inches. To convert to square feet divide by 144, so this is basically the 'face area' of the log in square feet.
Firstly, I find this more logical and hence easier to remember. Secondly, I find remembering the comparison between several logs easier if I just have to remember a smaller number in square feet, and then multiply by the length in feet to get cubic (Hoppus) feet.
Hope the above is clear!
An example of why.
Say I have a real log, rather than a neat, hypothetical cylindrical forest-grown log. It's 24' long and 2' dia or so for most of its length, with a severe narrowing to 18" about 16' up, due to a previous side branch.
If I'm looking at maximum use, I could treat it as two cylinders - first one has a mid quarter girth of 19", so an area of 361 square ins, or 2.5 square ft. Its volume is 2.5x16=40 Hoppus feet. The second one has a mid quarter girth of 14 ins, so an area of 196 square ins, or 1.36 square ft. Its volume is 1.36x8=11 Hoppus feet. This makes a total of 51 Hoppus feet.
However, say I want to consider using it as a full length beam. This means I can only use the smaller area, so already know its area (1.36 square ft) and just multiply by the length of 24ft to get 32.6 Hoppus feet. I now know I'm throwing away 18.4 Hoppus feet if I do this (or using them if I can as thinner boards etc).
I find this really useful in assessing potential ways of breaking down timber with step changes in diameter, bends and kinks, rot or other damage etc. but I have no idea if it helps you in the slightest!
Alec