I don't understand the question, what do you mean with "there are two intersection states between Q and the accepting states"? The definition of the successor states of the breakpoint construction is as follows for the pair of state sets (Q,Qf) we compute (suc∃(σ,Q),suc∃(σ,Q)∩F) if Qf={}, and otherwise (suc∃(σ,Q),suc∃(σ,Qf)∩F).