Select whichever preposition or determiner you consider the most appropriate for the blank space.
We met a very nice family__________ our holiday.

Correct option is C

The word that can be filled in the blank is ‘during’ to make the sentence grammatically and contextually correct.
• ‘During’ is used to indicate a period or range of time in which something occurs.
• As per the context, the word ‘during’ fits very well & hence, it is the correct option.
Meanings of other given words:
• While - used to talk about a period or situation when something is happening.
• Into - used to indicate movement toward or into something.
• By - used to show the means of achieving something.
• Thus, all the other given words have different meanings and do not fit in the context of the sentence.