The correct option is
A How many / could / was
The correct answer is Option A.
HOW MANY is used to ask the number/ quantity of something whose fixed number can be determined. There is a reference to the number of languages in the given sentence. This number can be determined. Thus HOW MANY is the correct answer.
COULD is the past tense of CAN. CAN means 'being able to'. The speaker is asking how many languages was Nicola able to speak when he was a child. There is reference to the past, thus the sentence is in the past tense. Therefore, COULD - the past tense of CAN is the correct answer.
WAS is the past tense of BE. The past tense will be used because the sentence is in the past tense.
The remaining options are incorrect because:
Option B: HOW MUCH is used when the exact number cannot be determined.
Option C & D are grammatically incorrect.