Finite automata to regular expression via state removal

Question

I am trying to convert this finite automata to a regular expression using state removal. When removing a state, I know that I should look at all outgoing and incoming transitions, and make sure sure that all paths though the soon to be removed state are preserved. However, I still find this entire concept a bit confusing. I have attached an image of a practice problem I've attempted, and I was wondering if it was correct. I would also appreciate any tips for tackling these types of problems.

Answer 1

I am not sure if this is a correct solution. (by the way I dont know if we can delete A at first step)