Final answer:
The correct answer is b. doubts; childhood. In this sentence, the tense being used is the past perfect continuous tense to describe an ongoing action that had been completed in the past.
Step-by-step explanation:
The correct option is: b. doubts; childhood. In this sentence, the verb "had been solving" indicates the past perfect continuous tense. The past perfect continuous tense is formed by using the past perfect of the auxiliary verb "to have" (had been) followed by the present participle of the main verb (solving). This tense is used to express an action that was ongoing and had been happening for some time before another action in the past. The sentence suggests that the nanny had been continuously solving the speaker's doubts throughout their childhood, emphasizing the duration and continuity of the action.