How did we get 24 hours in a day… why not 20 “hours” or 100 “hours” and why 60 seconds…
Now as far as the beer thing… 6 pack…tally whack why 24 beers in a case? 
Blame the Babylonians for the hour and minute thing. 24 is divisible by 2,3,4,6,8 and 12, more factors than any smaller number. 60 follows the same logic, since 60 is divisible by 2,3,4,5,6,10,12,15,20 and 30. This stuff is important when you live in a society that loves mathematics but hasn’t yet invented the decimal point. The Babylonians had numbering systems based on 24 and 60, much as our current system is based on 10. The Arabic system won out becuase the smaller base (as well as the invention of the number 0) made it was simpler to use.
The same divisibility favours 24 in the packing of beer bottles. A tidy arrangement of 6x4 is easy enough to stack and carry, and 24 beers is light enough for an adult to easily carry.
25 beers in a 5x5 box might work as well, but a long box is actually easier to carry than a square box (if you walk along carrying it, you rest it across your waist with your hands gripping the sides). Ideally, you want a box which is not much wider than shoulder-width, and not so long that carrying it forces your center of gravity forward, hurting your back. A 6x4 rectangle works nicely.