That code makes no sense. LIKE without a wildcard means equals, so the two conditions cancel each other out. Unless sock means color, in which case it would at best tell you what you have a set of. But for that, it would be much clearer to write:

SELECT sock
FROM socks
GROUP BY sock
HAVING COUNT(*) > 1
LIMIT 1;
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Of course, that completely ignores ids (which sock) and the state of the sock. At the very least, you ought to check for State = 'Washed' or MIN(Times_Worn).