You can get selected items from
var selectedQuery = listBox.Items.Cast<listitem>().Where(item => item.Selected);
And then put this in your textbox using String.Join().Hope you can understand what you need to do.
EDIT:
Alternately you can try..
string values = String.Join(" ", listbox.Items.Cast<ListItem>().Where(i => i.Selected).Select(i => i.Value).ToArray());