This is a complex sentence which consists of a dependent or subordinate clause and an independent clause.
'If you finish your yard work' -- dependent clause
'you can take the car to the movie' -- independent clause.
I would definitely go with B because a subjunctive is an realist mood (one that does not refer directly to what is necessarily real) – it is often contrasted with the indicative, which is a realist mood. Subjunctives occur most often, although not exclusively, in subordinate clauses, particularly that-clauses.
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Assuming that the underlined words it your brother's motor cycle,
i think it was a noun
It's thing that imposed to predicate done by the subject
Hope this helps