(Logic Question) Where am I going wrong in these deduction?

Question

I am trying to solve this:

1. (Premise 1) $A \vee B$
2. (Premise 2) $\neg B \vee C$

Prove: $A \vee C$

This is what I have done so far: First Try

Edit:2 Reached here

Answer 1

HINT

In the second subproof, that assumes $B$, you realized that you need the $\neg B \lor C$ premise to get to $A \lor C$ (you use it on line 8). However, instead of using Ana Con, you should use proper rules of inference. So ... set up a $\lor$ Elim on $\neg B \lor C$ ... but do it inside the subproof that assumes $B$!