16 men in 12 days can do 0.5work
1 man 1 day can do 0.5/(16x12) of a work
8days to do 0.5 of a work
1 man 8 days can do 8x0.5/(16x12) = 0.5x(1/24) of a work
... if you notice we need 24 men
... more detail
in8days, 0.5x(1/24) of a work need 1 man
in8days, 0.5 of a work need 0.5/(0.5x(1/24)) = 24 men
point is to find 'amount of work done per man per unit of time' then work out from that.