There are three cases:

1. Using no C's. That's the permutations of {S,O,E,R} or 4! = 24  

2. Using 1 C. We choose the other 3 letters from {S,O,E,R} in C(4,3)=4 ways
   That's 4·4! = 4·24 = 96 ways

3. Using 2 C's: We choose the other 2 letters from {S,O,E,R} C(4,2)=6 ways
   There are 2 indistinguishable C's, so that's 6· = 6· = 6·12 = 72 ways 

Answer = 24+96+72 = 192 ways.

Thanks to my computer program, here are all 192 in
alphabetical order 12 rows by 16  (12×16=192)

CCEO CCER CCES CCOE CCOR CCOS CCRE CCRO CCRS CCSE CCSO CCSR CECO CECR CECS CEOC
CEOR CEOS CERC CERO CERS CESC CESO CESR COCE COCR COCS COEC COER COES CORC CORE
CORS COSC COSE COSR CRCE CRCO CRCS CREC CREO CRES CROC CROE CROS CRSC CRSE CRSO
CSCE CSCO CSCR CSEC CSEO CSER CSOC CSOE CSOR CSRC CSRE CSRO ECCO ECCR ECCS ECOC
ECOR ECOS ECRC ECRO ECRS ECSC ECSO ECSR EOCC EOCR EOCS EORC EORS EOSC EOSR ERCC
ERCO ERCS EROC EROS ERSC ERSO ESCC ESCO ESCR ESOC ESOR ESRC ESRO OCCE OCCR OCCS
OCEC OCER OCES OCRC OCRE OCRS OCSC OCSE OCSR OECC OECR OECS OERC OERS OESC OESR
ORCC ORCE ORCS OREC ORES ORSC ORSE OSCC OSCE OSCR OSEC OSER OSRC OSRE RCCE RCCO
RCCS RCEC RCEO RCES RCOC RCOE RCOS RCSC RCSE RCSO RECC RECO RECS REOC REOS RESC
RESO ROCC ROCE ROCS ROEC ROES ROSC ROSE RSCC RSCE RSCO RSEC RSEO RSOC RSOE SCCE
SCCO SCCR SCEC SCEO SCER SCOC SCOE SCOR SCRC SCRE SCRO SECC SECO SECR SEOC SEOR
SERC SERO SOCC SOCE SOCR SOEC SOER SORC SORE SRCC SRCE SRCO SREC SREO SROC SROE

But the only ones that are really words are CORE, ORES, ROSE, and SORE,
but then EROS is the god of love, and maybe ROES are different kinds of fish
eggs.  There was a fictitious bird called a ROC, so if you had more than one of
them they would be ROCS. And of course a CROC is a crocodile. But I'm sure your
teacher didn't mean real words!  Hahahaha!

Edwin