I am a little confused by the quesiton, but I there is a very easy way to convert a LINQ query result to a list and that is to use the
ToList()
method.
The technolgy looks a lot like WPF or Silverlight. That means that you will have to set the ItemsSource for the ListBox to an IEnumerable of the class that contains the collection of objects with the properties category_name, item_name, and qty. This means that I am a little confused about the group by query. You don't need because you need tha category name. What I think you need is:
var query = from shoppingItem in db.Items
select new { shoppingItem.category_name,
shoppingItem.item_name,
shoppingItem.qty};
Pardon errors due to me not knowing everything about your problem.