Answer
The galaxy is $1.1\times 10^9~ly$ from the Earth.
Work Step by Step
(a) $\frac{\lambda_o-\lambda_r}{\lambda_r} = \frac{v}{c}$
$v = (\frac{\lambda_o-\lambda_r}{\lambda_r} )~c$
$v = (\frac{423.4~nm-393.4~nm}{393.4~nm} )~(3\times 10^5~km/s)$
$v = 22,900~km/s$
The galaxy is moving away from us at a speed of 22,900 km/s.
$d = \frac{v}{H_0} = \frac{22,900~km/s}{(21~km/s)/10^6~ly} = 1.1\times 10^9~ly$
The galaxy is $1.1\times 10^9~ly$ from the Earth.
