I do not know if this is a multiple choice question or not, but the answer is to end with his life by drinking the poisoned wine. Self-killing was widespread in ancient Rome, and it was considered neither shameful nor the result of a medical condition, particularly if it had been committed for ethical and reasonable motives. It was often referred to as a willing death. Famous statesmen, generals and philosophers, such as Brutus, Cassius, Cato the Younger, Socrates, and Seneca, among others, killed themselves - both Socrates and Seneca drank poison, like Horatio intended to do, but Cato stabbed himself and Brutus ran into his own sword. In this scene from Hamlet, the loyal Horatio, who knows that his beloved friend Hamlet will die, is showing his willingness to drink the remaining wine and die, to act more as an ancient Roman and not as a contemporary Danish, so that he does not have to live without his friend Hamlet, but the prince begs him not to do so, so he can tell his story.