24 Children can finish a work in = 12 days.
16 men can finish a work in  = 9 days.
So, in 12 days number of men who can finish the work = (16 X 9) / 12 = 12 men.
So, 24 Children = 12 men or 2 children = 1 man.
So, 12 men and 12 children = 12 men + 6 men = 18 men.
Now, 16 men can finish a work in = 9 days.
1 man can finish a work in = 9 x 16 days.
18 men can finish a work in = (9 X 16) / 18 = 8 days.