SQL query to look for a Kevin Bacon number of 2

To give a sketch of a solution rather than an exact solution I would use this general approach

SELECT *
FROM   ACTOR
WHERE  id IN (
SELECT id 
       /* ... of actors that have worked on a film worked 
         on by actors that have worked on a KB film*/
EXCEPT
SELECT id
 /* ... of all actors that have worked on a KB film
         including KB himself*/ )

Also as you are not allowed to use recursive CTEs anyway here's an answer using those.

WITH RecursiveCTE
     AS (SELECT C.pid,
                C.mid,
                0 as Level
         FROM   CASTS C
                JOIN ACTOR A
                  ON A.id = C.pid
         WHERE  A.fname = 'Kevin'
                and A.lname = 'Bacon'
         UNION ALL
         SELECT c1.pid,
                c2.mid,
                R.Level + 1
         FROM   RecursiveCTE R
                JOIN CASTS c1
                  ON c1.mid = R.mid
                     AND R.Level < 2
                JOIN CASTS c2
                  ON c1.pid = c2.pid)
SELECT *
FROM   ACTOR
WHERE  id IN (SELECT pid
              FROM   RecursiveCTE
              GROUP  BY pid
              HAVING MIN(Level) = 2)