A conjunction is a word used to connect other words, phrases or clauses.
Subordinating conjunction connects or joins an independent clause with a subordinate clause.
'While' means something that is happening at the same time as something else or indicates a contrast. In the given sentence, 'Peter came around' and 'we were eating' are the two activities happened at the same time.
'For' means the exact thing as because.
'In' is used as a preposition to denote a place.
'During' is a preposition used before a noun to say when something happens. It does not tell how long it happened.
Thus, option A is the correct answer.