Let the original number of women be $2 x$ and men be $3 x$, based on the initial ratio 2:3.
After 6 more men join, the number of men becomes $\(3 x+6\)$.
The new ratio of women to men becomes $1: 2$, so:

$$
\(\frac{2 x}{3 x+6}=\frac{1}{2}\)
$$


Cross multiply:

$$
\(\begin{gathered}
2 \times 2 x=1 \times(3 x+6) \\
4 x=3 x+6
\end{gathered}\)
$$


Subtract $3 x$ from both sides:

$$
\(x=6\)
$$


Original number of men is:

$$
\(3 x=3 \times 6=18\)
$$


Answer: There were originally 18 men in the group.