How to find a Cepheid's pulsation period using its graph?
This graph is not the light curve of a cepheid. It is used to find the average brightness of the star, and from that, estimate its distance.

The rate at which cepheids pulse is related to their average luminosity (and so their average absolute magnitude). This graph relates the period to their average absolute magnitude.

To use the graph, observe a cepheid for long enough to establish a period (say 30 days, for example). Then read the graph (an absolute magnitude of just under -5.5 in the example)

You now know how intrinsically bright the star is on average. By looking at its average apparent brightness, you can calculate an estimate of its distance. See How does the cepheid variables help in finding distance