If the wavelength of the red line of hydrogen coming from a galaxy is 654.3 nanometers instead of the normal 656.3 nanometers, is the galaxy moving towards the Earth or away from the Earth, is it red shifted or blue shifted, and how fast is it moving

The Doppler effect says that, if the source of light is moving towards the viewer, then the light will turn to the blue side (the wavelength decreases) if the source of light is moving away, then the light will turn to the red side (the wavelength will increase)

In this case, we have that the light that normally has a wavelength of 654.3 nm, now has 656.3 nm. So we can see that the wavelength increased, which means that the galaxy is moving away from the Earth, is red shifted and the velocity can be found by the equation:

(λ - λ₀) / λ₀ = v/c

Here we have that:

λ = 656.3 nm

λ₀ = 654.3 nm

c = 3.10^6 m/s

and v is the velocity of the galaxy.

(the fact that the units are different does not matter because the units cancel with the divisions)

(656.3 nm - 654.3 nm) / 654.3 nm = v/3*10^6m/s

0.003*3*10^6m/s = v = 9000 m/s