The carburetors on inboard mounted gasoline engines must be equipped with an approved back-fire flame arrestor. what purpose does having a back-fire flame arrestor play?

To prevent the ignition of gasoline vapors.

Explanation:

A back fire is an explosion that occurs in the air intake system by a running internal combustion engine.

Back-fire flame arrestor is a safety equipment used to prevent the ignition of gasoline vapour.

It stops the flame to avoid an engine backfiring and contact with other fuels. This can led to fire and heavy damage if back fire flame arrestors are not used.