Do it like this :
As said by Prerak, do the below in a DoubleClick event.
Add this to your constructor :
listBox2.MouseDoubleClick += new MouseButtonEventHandler(listBox2_MouseDoubleClick);
This is the function to implement it:
void listBox2_MouseDoubleClick(object sender, MouseButtonEventArgs e)
{
ListBoxItem item =(ListBoxItem)listBox2.SelectedItem;
Process.Start(item.Content.ToString());
}