How many detentions are there?
select distinct count ( * ) from detention
How many teachers are not involved in any of them?
select count ( * ) from ( select last_name from teachers except select t1.last_name from teachers as t1 join detention as t2 on t1.teacher_id = t2.teacher_id )
What are the last names of those teachers?
select last_name from teachers except select t1.last_name from teachers as t1 join detention as t2 on t1.teacher_id = t2.teacher_id