I need to show $\exists$ a surjective homomorphism $\phi:D\_8 \rightarrow C\_2 \times C\_2$

I have worked out that $\langle\rho^2\rangle$ $\triangleleft$ $ D\_8$ and that

$\displaystyle \frac{D\_8}{\langle\rho^2\rangle} \cong C\_2 \times C\_2$

The solution is as follows:
![enter image description here](https://i.stack.imgur.com/4cjnO.jpg)

I do not follow the part highlighted in green.