24 men can complete a work in 16 days

\(\therefore\) 1 man’s 1 days’ work = \(\frac{1}{24\times16}\) 

\(\therefore\) 12 men’s 1 day’s work = \(\frac{12}{24\times16}\) = \(\frac{1}{32}\)

18 women can complete the work in 32 days

\(\therefore\) 1 woman’s 1 days’ work = \(\frac{1}{18\times32}\)

\(\therefore\) 6 women’s 1 day’s work = \(\frac{6}{18\times32}\) = \(\frac{1}{96}\)

\(\therefore\) (12 men’s + 6 women’s) 16 days’ work = 16 x \(\big(\frac{1}{32}+\frac{1}{96}\big)\) = 16 x \(\big(\frac{3+1}{96}\big)\)

= 16 x \(\frac{4}{96}\) = \(\frac{2}{3}\)

\(\therefore\) Remaining work = 1 - \(\frac{2}{3}\) = \(\frac{1}{3}\)

(12 men’s + 6 women’s) 2 days’ work = 2 x \(\big(\frac{1}{32}+\frac{1}{96}\big)\) = 2 x \(\big(\frac{4}{96}\big)\) = \(\frac{1}{12}\)

Remaining work = \(\frac{1}{3}\) - \(\frac{1}{12}\) = \(\frac{3}{12}\) = \(\frac{1}{4}\)

\(\therefore\) \(\frac{1}{384}\) work is done in 1 day by 1 man

\(\therefore\) \(\frac{1}{12}\) work will be done in 2 days by \(\big(384\times\frac{1}{12}\times\frac{1}{2}\big)\)men = 16 men.