smc

If we let $p$ be the number of people initially in the group, then $0.4p$ is the number of girls. If two girls leave and two boys arrive, the number of people in the group is still $p$, but the number of girls is $0.4p-2$. Since only $30\%$ of the group are girls, $$\begin{array}{rl}\frac{0.4p-2}{p}& =\frac{3}{10}\\ 4p-20& =3p\\ p& =20\end{array}$$ The number of girls initially in the group is $0.4p=0.4(20)=\boxed{8}$