This line
if (!ListBox2.Items.Contains(listItems))
is checking if the Items collection contains the listItems object, which is doesn't as you have just created it, you haven't added it to the Items collection. What you really want to do is check if ListBox2.Items has a ListItem that has "y" as it's value.
if (ListBox2.Items.FindByValue(listItems.Value) == null)
There is also a FindByText function if that's what you're after.