The sample demonstrates how to navigate through the list items using the Keyboard

Tab - Like other widgets, the jqxListBox widget receives focus by tabbing into it. Once focus is received, users will be able to use the keyboard to change the jqxListBox's selection. A second tab will take the user out of the widget.
Shift+Tab - reverses the direction of the tab order. Once in the widget, a Shift+Tab will take the user to the previous focusable element in the tab order.
Up/Down arrow keys - select previous or next item.
Page Up/Page Down keys - navigate up or down with one page.
Home/End keys - navigate to the first or last item.
Hold SHIFT and press Up or Down arrow keys to select multiple items.
Hold SHIFT or Ctrl and click with the mouse to select multiple items.
Incremental Search - start typing to select the matching item.
First letter - press a key to navigate to a matching item. Subsequent press on the same key will iterate over the matches.