The correct answer is A. The hardware on the cabinets need to be removed before we paint them.
This is because the subject of the sentence is hardware (a singular subject) and the verb is conjugated for a plural subject.
In this example, it is easy to get confused and think that this sentence is correct if you thought that the plural noun cabinets was the subject. To avoid this confusion, we can eliminate prepositional phrases like “on the cabinets” when we are checking for subject-verb agreement to simplify the sentence.
Hope this helps!