In this scenario, You need perform some string operations with custom implementation. You can get you listbox items into a collection and perform split operation to seperate year and month values. You can get the listbox items like
string[] names = listBox1.Items.Cast<string>().ToArray();
You can get the month number with the below code.
int month = DateTime.ParseExact(MonthNameStr, "MMMM", CultureInfo.CurrentCulture).Month;
After splitting, populate the collection then apply sort and then assign as datasource to listbox.