Displaying Taxonomy on the menu
The reason the Samsung Air Conditioner Unit was not showing as we clicked on the category was because we inserted as  Product Categories\Air Conditioner\Air Conditioning Unit instead of Product Categories\Air Conditioning Unit.

The subcategory Air Conditioner was not defined.  So, drupal did not know how to display it.  Once we moved to Product Catogoies\Air Conditioning Unit, it displayed.  

Now, the task is how to create the subcategory Air Conditioners so that we could insert Air Conditioner Unit there instead of inserting it directly under Product Categories.