Answer
The distance between the Earth and galaxy A at the time of detection is $~~9.9\times 10^8~ly$
Work Step by Step
We can find the distance between the Earth and galaxy A at the time of detection:
$d = r+r~H~\Delta t$
$d = (6.6\times 10^8~ly)+(6.6\times 10^8~ly)~(0.0218~m/s~ly)~(6.9\times 10^8~years)$
$d = (6.6\times 10^8~ly)+(6.6\times 10^8~ly)~(0.0218~m/s~ly)~(6.9\times 10^8)(365)(24)(3600~s)$
$d = (6.6\times 10^8~ly)+(3.107\times 10^{16}~m)$
$d = (6.6\times 10^8~ly)+(3.107\times 10^{16}~m)(\frac{1~ly}{9.461\times 10^{15}~m})$
$d = 9.9\times 10^8~ly$
The distance between the Earth and galaxy A at the time of detection is $~~9.9\times 10^8~ly$
