=IF

This question is very unclear. What do you mean by "then do another search at the end?"
You can 'chain' IF statements:
=IF(AND(G4="class",K4="c7"), "10", IF(AND(G4="free",K4="d8"), "25", ""))
so in this case IF the first case is FALSE then it falls into the second IF case
you could also use IFS to this multi-case also.
or if you want a second case in either result to be 'tacked' on you can add that
=IF(AND(G4="class",K4="c7"), "10", "") & IF(AND(G4="free",K4="d8"), "25", "")
in this case with will & the result from the first to the result from the second. note in this case the result will be exactly the same as the above 'chain' version since both AND versions can't be both true so only one or neither will show