Question

With advances in telescope technology, we can see that galaxies are moving _______ over time.. A closer to each other . B farther away from each other . C in random directions

Answer 1

With advances in telescope technology, we can see that galaxies are moving : B. Farther away from each other

This was first discovered by Edwin Hubble during his observation. From his observation he saw that some objects that he observed became smaller and smaller. Which is a sign that it moved farther away from each other

hope this helps

Answer 2

As someone else said, in small regions they do all of the above, but in general terms they are moving farther away from eachother. 
This discovery from Hubble was what lead us to the understanding that the universe was at one point in time, all at one infinitly small but dense singularity, which is how we came up with the Big Bang Theory.