If we could split boys and girls into n teams, and b boys and g girls will be in each team, then obviously `nb=48` and `ng=60.` Therefore `n` divides 48 and `n` divides 60, or the same may be formulated as "`n` is a common divisor of 48 and 60". And the greatest such number is the greatest common divisor (GCD) of 48 and 60.
One way to find it is to factor 48 and 60 into prime factors:
There are common prime divisors `3` and `2^2,` GCD is their product which is `12.`
So the answer is: 12 commands is the maximum. Each of them will consist of 48/12=4 boys and 60/12=5 girls.