。
Do ghosts really exist, I wonder.
Literal
Ghosts [topic-は] really exist-[nominal-のだろうか]?
のだろうか is the questioning version of のだ — 'is it the case that...?' Often used for self-reflective wondering about abstract or metaphysical matters. 居る ('to exist') here is used for the ghosts as animates, even though they're supernatural — choice of いる vs ある marks the speaker as treating ghosts as sentient entities. Slightly philosophical.