Well, it's theoretically possible to do something like this using ORDER BY and LIMIT clauses in your DELETE query, but it's a really bad idea. SQL is set-oriented, and sets, by definition, do not have an ordering. So saying "delete the third item in this table" doesn't really make sense because "third item" is not strictly defined.
What you really want to do is to delete items based on their primary key. If the table doesn't have a primary key, then you should add one. It will give you better performance and more data integrity than trying to rely on offsets in result sets.
As far as code goes, all you need to do is to set up your form so that the check boxes in your table pass back the primary key values to your database access layer. Then you can just delete a particular record with a simple simple "DELETE FROM dbtable WHERE id = $keyval", or something along those lines.