Well, there's no relevance to a record's row position in a database. If you have them lettered or numbered with a column like you show here, you could just swap the letters or numbers with each other and then re-sort the recordset. Depending on how fancy you want to get, that could just be a matter of using input boxes and a pushbutton, or using jscript to do that for you. You'd save changes to the recordset, and post the form back to the same page.
There may be other ways of doing this. I would suggest you post the question to www.aspmessageboard.com.