You can save a structure from within a structure only in the very limited case that the parent structure is a scalar structure array and that all fields within the parent structure are to individually become variables in the mat file. The handles structure is a scalar structure so it meets the first requirement but it is quite unlikely that you want to save all parts of it to become individual variables.
It is likely that you will need to save the content of the substructure to a variable and then save the variable.
Car = handles.Car;
save(FullPath, 'Car')
The one exception I mentioned would look like
save(FullPath, '-struct', 'handles')
