What are four events that happen to Bilbo where his feelings change in The Hobbit?
I am guessing that your question is referring to how Bilbo changes from the security-loving Hobbit at the beginning of the novel to the adventure-seeking hero at the end of the novel. For this, you really need to re-read the book noting down and tracing his development as a character, focussing on key stages. I am not going to give you four stages but I will focus on one and talk about how this changes Bilbo and crucially helps him realise certain truths about himself.
To me, a crucial episode occurs when Bilbo rescues the dwarves from the spiders in Chapter 8. We see how he independently and without any help has to come up with a plan and execute it to free his friends and stop them getting eaten by the spiders. He takes charge and leads the somewhat befuddled dwarves as they wake up and try to fight off the spiders. Note how this is the first time that Bilbo has really had to do this to protect others - he certainly has had to use his wits to protect himself against Gollum, but this is the first time he successfully saves his companions. Compare this event to the troll incident, for example. But most importantly, notice how the dwarves change their opinion of Bilbo:
Knowing the truth about the vanishing did not lessen their opinion of Bilbo at all; for they saw that he had some wits, as well as luck and a magic ring - and all three are very useful possessions. In fact they praised him so much that Bilbo began to feel there really was something of abold adventurer about himself after all, though he would have felt a lot bolder still, if there had been anything to eat.
So note how this represents a crucial stage in Bilbo's "journey" - now re-read the novel and see what other stages you can identify, focussing on how they develop Bilbo's character.