The correct answer to this question is B, WAS HOOVERING. The keyword in this sentence to help answer this question is the word yesterday. This word is past tense and is used to describe the day before the current moment.
Therefore, the action of the sentence must be past tense as well for it to be grammatically correct. A and D are present tense so that they wouldn't be correct. Answer C is also past tense, but the word was used to describe plural subjects. The subject of the sentence is "my mother," and this is a singular subject, which eliminates answer C and leaves answer B as the correct one.
My mother WAS HOOVERING the carpet when I got home yesterday afternoon. (When you say 'yesterday afternoon', it means it already passed, so the possible answers are either Were hoovering or Was hoovering, but since the subject is 'mother' and it is singular, so the answer is WAS HOOVERING)