# Original distance from us to galaxy at redshift of z=6 if we know the current distance and taking into account universe expansion?

So I'm given that a galaxy cluster is currently at redshift z = 6 and the question asks "what was its distance from us at the time the light left the cluster?"

We only know the redshift, but the question assumes we are able to look up its current distance from us, which Wikipedia states is about 322.9 million light years (Coma Cluster).

Any ideas?

First of all, the Coma cluster has a redshift of $z\sim 0.02$, not $6$. The galaxy cluster at $z=6$ must be some other cluster, or a hypothetical one imagined for this exercise.
To find the distance at the time the light was emitted, you can first find the distance today (either the "proper distance" or the "comoving distance", these are equivalent at the present day). To then get the proper distance at $t(z=6)$, simply multiply by the scale factor $a(z) = \frac{1}{1+z}$ at $z=6$.
The comoving distance to an object at redshift $z$ is: $$d_C(z)=\int_0^z\frac{c\,{\rm d}z'}{H(z)}$$ where $H(z)=H_0E(z)$ is the Hubble parameter for whichever cosmology you're interested in.