Answer
The distance to the galaxy is $~~2.80\times 10^8~ly$
Work Step by Step
We can find the radial velocity of the galaxy relative to us:
$v = \frac{\lambda-\lambda_0}{\lambda_0}~c$
$v = \frac{602.0~nm-590.0~nm}{590.0~nm}~c$
$v = 0.0203~c$
We can find the distance to the galaxy:
$Hr = v$
$r = \frac{v}{H}$
$r = \frac{(0.0203)~(3.0\times 10^8~m/s)}{0.0218~m/s~ly}$
$r = 2.80\times 10^8~ly$
The distance to the galaxy is $~~2.80\times 10^8~ly$
