Db2 select query with group by clause throws error?

If you want "distinct values of SERIAL_NUM and EMP_NAME" you need to tell the database which notesid to pick if there are multiple combinations of serial_num and emp_name. If you don't care which notesid you get, you can e.g. use min()

SELECT serial_num,
       emp_name,
       min(notesid) as notesid
FROM db2inst1.emp_hc 
WHERE func_vp ='Bob '  
  AND vice_pres ='Bob'  
  AND director ='Michael'  
  AND third_line ='Linda'  
GROUP BY serial_num,emp_name