You offer the neighbor $50, the monetary value you put on your sleep, to never play his music between midnight and 7 AM. By doing so A) you have failed to bring about an efficient solution since you should have complained to the police.
B) you have indicated the cost of the externality. The externality is not internalized even if he accepts your offer.
C) you have indicated the cost of the externality, which internalizes the externality.
D) you have indicated a willingness to make the external cost a social cost.