The problem appears to be the NORMALS for the chassis (outside part im not a car guy so im not sure what's best to call it).
1st try to export the model as a .OBJ file and see if it still appears (sometimes OBJ's are exported with different settings).
If that works then your good, but im assuming there is a specific reason you wish to use FBX (animation etc), so perhaps try to reverse the normals on your model.