When you are grouping by some column(s) value, then you may select only those column(s) in the SELECT statement. You can not SELECT any column(s) those are not in GROUP BY clause. In you statement, you are grouping by r.Bfid, but, selecting f.bfid. This is not allowed. Just think it yourself why non GROUP BY column(s) are not allowed in SELECT statement.
I have changed the query. Check this.
select distinct avg(r.rate) As Rate, r.Bfid as BFid
FROM bthfac AS f,batch b,facfeedback r where f.facid= '60,75,6'
and f.Bthid=b.Bthid and r.bfid = f.bfid and b.class= 'PST'
and year(b.examdate)= '2011' and month(b.examdate)= '10' Group By r.Bfid