The private pilot receiving instruction reported that during the proficiency training flight, he was seated in the right front seat position while the flight instructor was in the left seat. Following a normal approach for landing, he felt the airplane begin to sink about three to five feet above the runway and attempted to compensate with flight control inputs. The pilot stated that the "automatic (almost subconscious) reaction was to push in the throttle with his right hand and pull back on the yoke with his left hand slightly," which, due to his right seated position, resulted in his right hand pushing the nose down and his left hand pulling back on the throttle thus reducing power. Subsequently, the airplane struck the ground and bounced back into the air. The pilot initiated a go-around followed by the flight instructor taking control of the airplane and landing uneventfully. Post accident examination of the airplane by the pilot and an airframe and power plant mechanic revealed that the engine firewall was structurally damaged. The pilot reported that there were no mechanical anomalies that would have precluded normal operation of the airplane at the time of the accident.