24 men can complete a work in 16 days, thus one man's work progress each day = 1/(16*24)

women can complete the same work in 24 days, thus one woman's work pregress each day = 1/(24*32),

16 men and 16 women started working and worked for 12 days, their progress now = 16*12*1/(16*24) + 16*12*1/(24*32) = 1/2 + 1/4 = 3/4,

now they need to finish the rest of work 1-3/4=1/4 in 2 days,

thus the number of men = 1/4 / [1/(16*24)] = 96 men.