The flight instructor reported that, during an instructional flight, he told the student to set up for landing on runway 6. When they were at an altitude of about 400 ft above ground level, the flight instructor told him to apply full power since for a go-around. When the student applied full power, the engine did not respond. The flight instructor took control of the airplane and tried to land on runway 24. The flight instructor knew they would not make the runway, so he tried to land in the grass and the left wing contacted a fence and flipped the airplane over, which resulted in substantial damage to both wings, the vertical stabilizer and horizontal stabilizer. The flight instructor stated that he thought the throttle cable had become disconnected. A postaccident examination revealed that the throttle cable was not connected to the carburetor. An AN drilled bolt was found at the bottom of the cowling; however, the castellated nut was not located. Review of the maintenance logbooks revealed that the engine had been recently overhauled and installed in the airplane. Further conversations with the flight instructor, who was also the mechanic, stated that it is possible he forgot to install the cotter pin into the castellated nut and the bolt fell out.