The multitudes just asked what to do to do the works of God, and Jesus talked about how the "work of God" is believing in Jesus. The multitudes' question is now regarding what to do to believe in Jesus. In particular, they asked Jesus what sign He will do, knowing the Exodus story of manna (6:30-31).
Keep in mind that much of the multitudes have experienced Jesus feed 5000 from a bag of lunch. However, it's implied that the peeps wanted more sights to help convince them -- especially sights comparable to the manna feat.
In response to the comment on the manna, Jesus talked about the source of the bread from heaven. While Moses did delivery, God was the one who sent bread from heaven. In fact, since Moses is a historical figure, Moses did not give the multitudes of Jesus's time bread from heaven -- but God the Father can still do so. Additionally, Jesus talked about how the "bread of God" is one who is sent by the Father, "comes down from heaven", and "gives life to the world" (6:32-33). At this time, Jesus was already using figurative language with bread imagery -- and he would continue to do so.