This is an inverse proportion problem. The amount of work is constant. If you increase the number of workers, the time taken to complete the work will decrease proportionally, assuming constant efficiency.

Let $\(M_1\)$ be the initial number of men and $\(D_1\)$ be the initial number of days.
Let $\(M_2\)$ be the new number of men and $D_2$ be the new number of days.
The relationship for this type of problem is:

$$
\(M_1 \times D_1=M_2 \times D_2\)
$$


Given:
- $\(M_1=9\)$ men
- $\(D_1=12\)$ days
- $\(M_2=24\)$ men
- $\(D_2=\)$ ? days

Substitute the given values into the formula:

$$
\(9 \times 12=24 \times D_2\)
$$


Now, solve for $D_2$ :

$$
\(\begin{aligned}
& 108=24 \times D_2 \\
& D_2=\frac{108}{24}
\end{aligned}\)
$$


To simplify the fraction:
Divide both by 12 :

$$
\(\begin{aligned}
& D_2=\frac{108 \div 12}{24 \div 12}=\frac{9}{2} \\
& D_2=4.5 \text { days }
\end{aligned}\)
$$


So, it will take 24 men 4.5 days to complete the same piece of work.