On August 17, 1998, at 1332 central daylight time, a Beech C23, N6756C, sustained substantial damage, during an aborted landing following an approach to runway 12L (8,000' X 150' dry/concrete), at North Platte, Nebraska, and impacted the terrain. The pilot said that she lost control due to a crosswind condition. The student pilot reported no injuries. The solo instructional 14 CFR Part 91 flight was operating in visual meteorological conditions. No flight plan was on file. The local flight departed at 1215. The pilot said that during her initial attempt to touchdown, she was unable to maintain directional control. She said she added power in an attempt to regain directional control. She said that she then attempted to abort the landing, reducing from full flaps setting to one half. She said she was unable to gain altitude. She said that she did not recall the plane touching the ground until it came to rest. Subsequent to the accident, an examination of the accident site revealed that after the airplane departed the runway to the right. It crossed a taxiway and proceeded through a grassy area for approximately 600 feet, where the airplane turned left, and the left main landing gear and nose gear collapsed. At time of the accident the airplane was landing on runway 12L. Winds recorded at the accident site 36 minutes prior to the accident were 140 degrees at 8 knots.