Greater red shifts in the spectra of galaxies indicate

The correct answer is "faster speeds".

Explanation:

Red shift: Light changes as the object in space (such as galaxy or star) moves away from us then the light is shifted to red end. In this case, the light is shifted to longer wavelength or the light shifted to a shorter frequency.

Faster the galaxy is moving away from the observer then there will be greater red shift. Slower the galaxy is moving away from the observer then there will be lesser red shift.

Therefore, Greater red shifts in the spectra of galaxies indicate faster speeds.