Find four rational numbers between $\frac{2}{9}$ and $\frac{2}{7}$

$\frac{2}{9}=\frac{2 \times 7}{9 \times 7}=\frac{14}{63}$ and $\frac{2}{7}=\frac{2 \times 9}{7 \times 9}=\frac{18}{63}$

Also, $\frac{14}{63}=\frac{14 \times 2}{63 \times 2}=\frac{28}{126}$ and $\frac{18}{63}=\frac{18 \times 2}{63 \times 2}=\frac{36}{126}$

Now,

$28<29<30<31<32<33<34<35<36$

$\therefore \frac{28}{126}<\frac{29}{126}<\frac{30}{126}<\frac{31}{126}<\frac{32}{126}<\frac{33}{126}<\frac{34}{126}$ $<\frac{35}{126}<\frac{36}{126}$

Thus, we get seven rational numbers between $\frac{28}{126}\left(\frac{2}{9}\right)$ and $\frac{36}{126}\left(\frac{2}{7}\right) .$ Any four of those numbers is the desired four numbers.

So, $\frac{29}{126}, \frac{30}{126}\left(\frac{5}{21}\right), \quad \frac{31}{126}, \frac{32}{126}\left(\frac{16}{63}\right)$ are four among the infinitely many rational numbers between $\frac{2}{9}$ and $\frac{2}{7}$.