Question

hubble measured the velocity of the movement of galaxies by using
hubbles law states that galaxies located farthest from the center of the universe than those closest to the center.

Explanation:

For the first blank: Hubble measured the velocity of galaxy movement using the Doppler effect (specifically redshift, which is analyzed via spectroscopy). The Doppler effect (redshift) allows measuring how fast galaxies are moving away by the shift in spectral lines.
For the second blank: Hubble's law states that the velocity of a galaxy's recession is proportional to its distance from us (or the center - in the context of the expanding universe, all galaxies are moving away, and farther ones move faster). So galaxies farthest from the center (or us) move faster than those closest.

Answer:

First blank: Doppler effect (or redshift/spectroscopy, but most precisely, the Doppler effect - redshift analysis).
Second blank: move faster