Complex sentence: Inside of the compound, Checque, who was the point man, was shot by a Taliban fighter from inside the single room holding the hostages, undeterred, Byers burst into the room, shooting dead an armed Taliban fighter.
Split into simpler sentences: Inside of the compound, Checque, who was the point man, was shot by a Taliban fighter from inside the single room holding the hostages. Undeterred, Byers burst into the room, shooting dead an armed Taliban fighter.