We let the time taken when ....
the larger hose alone is used be x - 6
and the smaller hose as x.
This would make their rates
Take note that:
1 / rate = time
1 / rate of both hoses = 4
rate of both hoses = 1/4
This would mean that x = 12 or 2 but x cannot be 2 since that would make the time taken for the larger hose negative.
Therefore it will take the smaller hose 12 hours to fill the swimming pool alone.