If 4 men or 6 women can do a piece of work in 24 days, then the no. of men should accompany 3 women to complete the work in 16 days is

4 men$\to 24\text{\hspace{0.17em}days}$

4 men $\to 1\text{day work=}\frac{1}{24}$

1 men $\to 1\text{\hspace{0.17em}day work}=\frac{1}{24\times 4}$

$\Rightarrow 6\text{\hspace{0.17em}women}\to 24\text{\hspace{0.17em}days}$

6 women $1\text{\hspace{0.17em}day\hspace{0.17em}work}\to \frac{1}{24}$

1 women $\to 1\text{\hspace{0.17em}day\hspace{0.17em}}=\frac{1}{24\times 6}$

Number of men $=x$

$\Rightarrow \frac{x}{24\times 4}+\frac{3}{24\times 6}=\frac{1}{16}$

$\Rightarrow \frac{3x+6}{24\times 12}=\frac{1}{16}$

$\Rightarrow 3x+6=\frac{24\times 12}{16}$

$\Rightarrow 3x=18-6$

$\Rightarrow 3x=12$

$\Rightarrow x=4\text{\hspace{0.17em}men}$