The correct option is
C The film had already begun.
The given situation states a past event 'went to the cinema last night'.Option C: 'Had already begun' is in past perfect tense. It states an action that completed in the past.
The past perfect tense indicates that an action completed 'film had already begun' before another action took place 'you arrived at the cinema late'.
Hence this option is relevant in meaning and C is correct.
Option A: 'Has already begun' is in present perfect tense. It states an action that has just happened. But the situation has already happened in the past 'last night'.
Option B: 'Began' is a simple past tense verb. It states an action that has happened, but does not indicate when. The past perfect 'had already begun' indicates that the action happened before 'you went to the cinema'. So, the more suitable tense is past perfect.
Option D: 'Will' is in the future tense.
It states an action that is yet to happen, as opposed to the past situation.
Also, 'already' itself refers to 'past or present', so 'will' and 'already' do not form a complete meaning.
Hence options A, B and D are incorrect.