In Julius Caesar, how does the appearance of Caesar's ghost foreshadow Brutus' death?
Caesar's ghost appears to Brutus in act 4, scene 3. In that scene, the ghost tells Brutus that he will see him at Philippi. This is significant because the Battle of Philippi is where Brutus and Cassius battle Mark Antony and Octavius to the death.
The Battle of Philippi is also a historic battle. You can read all about it from the link below. In Shakespeare's plays, the appearance of a ghost often foreshadows death. In this case, Caesar's ghost tells Brutus that he will see him at Philippi. This is a bad sign for Brutus, and the frightening vision is further reinforced by Cassius spotting ravens, kites, and crows in Philippi in act 5, scene 1. The appearance of birds of prey on a battlefield is a bad omen in Shakespearean plays, symbolizing imminent death and destruction.
The appearance of Caesar's ghost also rebukes Brutus's later stalwart pronouncement that he would never commit suicide in act 5, scene 1. For all intents and purposes, Brutus never intended to lose the war. However, the appearance of the ghost prior to the Battle of Philippi tells us that Brutus's cautious optimism has not served him well. In act 5, scene 5, Brutus finally reveals that Caesar's ghost appeared to him twice, once in Sardis and once in Philippi. At this point, Brutus is convinced that his "hour [has] come," and he enlists Strato's help in committing suicide.
I'm not sure it foreshadows Brutus' death, as such, but it is certainly associated with it: at least, in Brutus' mind. Shortly before Brutus' suicide, he openly admits that it is partly to do with the fact that he has seen Caesar's ghost.
Why, this, Volumnius:
The ghost of Caesar hath appear'd to me
Two several times by night; at Sardis once,
And this last night here in Philippi fields.
I know my hour is come.
Brutus clearly feels somewhere that the murder of Caesar needs to be revenged with his own death, as he suggests in his funeral speech. And, when the ghost does appear, Brutus asks it directly
Art thou some god, some angel, or some devil
That makest my blood cold, and my hair to stare?
Speak to me what thou art.
Is it a figment of Brutus' guilty imagination? Is it a real ghost come to revenge Brutus? Who knows. But it certainly becomes associated in Brutus' own mind with his death.
Hope it helps!