remove handles

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and clean with paint thinnner or something like murphys oil soap or simple green

reinstall handles

if you want to refinish, its time consumeing and involved, do a internet search on google.com keyword cabinet refinishing

suggestion, remove all hardware, handles, hinges, do the doors on saw horses, cabinets where they are rehang when done

doing the insides is even more work. you may wish you never started, so try cleaning first

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