Answer
The distance to the galaxy when the light was emitted was $~~1.38\times 10^{10}~ly$
Work Step by Step
We can find the radial speed of the galaxy relative to us when the light was emitted:
$v = \frac{\Delta \lambda}{\lambda_0}~c$
$v = \frac{2.00 \lambda_0-\lambda_0}{\lambda_0}~c$
$v = c$
We can find the distance to the galaxy when the light was emitted:
$v = H~r$
$r = \frac{v}{H}$
$r = \frac{3.0\times 10^8~m/s}{0.0218~m/s~ly}$
$r = 1.38\times 10^{10}~ly$
The distance to the galaxy when the light was emitted was $~~1.38\times 10^{10}~ly$
