Arbitrarily choosing to keep the minimum PIC_ID. Also, avoid using the implicit join syntax.
SELECT U.NAME, MIN(P.PIC_ID)
FROM USERS U
INNER JOIN POSTINGS P1
ON U.EMAIL_ID = P1.EMAIL_ID
INNER JOIN PICTURES P
ON P1.PIC_ID = P.PIC_ID
WHERE P.CAPTION LIKE '%car%'
GROUP BY U.NAME;