The correct option is
B Finally
Option B is the correct answer because 'once and for all' means completely and finally.
Options A, C and D are incorrect because 'authoritatively' means in a way that shows you are confident, in control, and expect to be respected and obeyed, 'angrily' means in a way that shows that you feel angry with someone or about something and 'coldly' means in an unfriendly way and without emotion.
Option E is incorrect because the correct answer has already been chosen.