Now that the multitudes heard how the Father gives bread, they wanted the Lord to always give such bread!
Jesus replied on how He is "the bread of life". Whenever someone comes to Jesus, that person "shall never hunger", and whenever someone believes in Jesus, that person "shall never thirst" (6:35). Considering that Jesus personifies bread, Jesus does not literally mean that such people would not have to eat or drink again on Earth, but Jesus means that certain needs will be fully met.
Which needs? Remember that back in 6:26-27, Jesus talked about how the multitudes were filled and how some food perishes but the food from the Son of Man lasts for everlasting life. Thus, Jesus provides the need to be filled for everlasting life, and as we'll see much later, he accomplished it through the cross/resurrection (with the resurrection demonstrating Jesus's power over death). From John 3, the everlasting life is linked to being "born again". The need for everlasting life implies that before being filled, we don't have everlasting life. Also from John 3, all of us need some sort of renewal (and if we're honest, we have done screw-ups in the past) -- especially since we have some brokenness from said screw-ups. In fact, our brokenness from our screw-ups actually keeps us from having everlasting life (much like how a broken car eventually wears down).
Additionally, Jesus mentioned how the multitudes saw Jesus yet haven't believed in Him (6:36). The statement suggests that Jesus said what he said in 6:35 so the multitudes can believe in him. In fact, from 6:35, believing in Jesus is how we can be filled, and as stated later, all believers will come to Jesus. Believing in Jesus is accepting that we need Lord Jesus (who is Son) as the "bread of life" and counting on Jesus for fulfilling the need to be filled for everlasting life (via His death on the cross and resurrection). That's it for us. Jesus as Lord (and Son) gives us eternal life as the bread of life and Jesus as Savior saves us from a scenario where we don't have everlasting life.
For the readers who decided to accept Jesus and count on Him for saving us, you are guaranteed everlasting life. I don't have a "I raise my hand" button or "I accepted Jesus" button because faith starts internally. (You can raise your hand though.)