Fill in the blank with the most appropriate word from the options giv…

The correct answer is Option (2) → at

Preposition with an event:

• At is used for an event or occasion where people gather: at a party, at a meeting, at a wedding.
• In is used for the inside of a place, and on for a surface or a day.
• This sentence: the friends were met during the party, an event, so the preposition is at; "in the clubhouse" then gives the place.
• Complete sentence: Did you meet your friends at the party in the clubhouse?
  Example: We met our old teacher at the wedding.

Why the Other Options are Incorrect?

Option 1: in — Incorrect. In shows position inside a place or space; "in the party" is used for a member of a political party, not for attending an event.
Example: The children are playing in the garden.

Option 3: on — Incorrect. On shows a surface or a day; it is not used for an event such as a party.
Example: The keys are on the table.

Option 4: for — Incorrect. For shows purpose; "meet your friends for the party" would mean meeting them in order to go to the party, not meeting them there.
Example: She bought a new dress for the party.