。
Proving that ghosts exist is difficult.
Literal
Ghosts [subject-が] exist-[nominal-こと] [object-を] prove-[nominal-のは] difficult.
Two nominalizations stacked: first ことを ('the fact that X'), then のは ('the act of X-ing') to topicalize the whole proof action. Note how in subordinate clauses, 幽霊 is marked with が, not は — subordinate subjects use が in Japanese. 証明する ('to prove, demonstrate') is formal vocabulary.