What happened
The FAA’s narrative, in sentence case. The FAA writes it in capitals and removes private details.
While performing the run-up checklist, the engine quit during the idle check. An unsuccessful attempt was made to restart the engine a few seconds after it quit, and after a brief pause another attempt was initiated which resulted in a "backfire-like sound" coming from the bottom left side of the cowling and smoke coming off the left side of engine. Pilot completed the engine fire during start checklist and instructed student pilot to leave the aircraft. After pilot finished the checklist and left the aircraft with the fire extinguisher the fire had already extinguished. Airport fire and rescue attended the aircraft, but no assistance was needed. Aircraft was towed back to the privacy data omitted ramp.
As the FAA filed it
WHILE PERFORMING THE RUN-UP CHECKLIST, THE ENGINE QUIT DURING THE IDLE CHECK. AN UNSUCCESSFUL ATTEMPT WAS MADE TO RESTART THE ENGINE A FEW SECONDS AFTER IT QUIT, AND AFTER A BRIEF PAUSE ANOTHER ATTEMPT WAS INITIATED WHICH RESULTED IN A "BACKFIRE-LIKE SOUND" COMING FROM THE BOTTOM LEFT SIDE OF THE COWLING AND SMOKE COMING OFF THE LEFT SIDE OF ENGINE. PILOT COMPLETED THE ENGINE FIRE DURING START CHECKLIST AND INSTRUCTED STUDENT PILOT TO LEAVE THE AIRCRAFT. AFTER PILOT FINISHED THE CHECKLIST AND LEFT THE AIRCRAFT WITH THE FIRE EXTINGUISHER THE FIRE HAD ALREADY EXTINGUISHED. AIRPORT FIRE AND RESCUE ATTENDED THE AIRCRAFT, BUT NO ASSISTANCE WAS NEEDED. AIRCRAFT WAS TOWED BACK TO THE ^PRIVACY DATA OMITTED^ RAMP.