좋아해하셔 is composed as 좋아해하(다) + 시 + 어 좋아해하다 is composed as 좋아(하다) + 해하다 해하다 is used after an adjective which ending is 하다 ex) 느긋해하다 is composed as 느긋하(다) + 어/여 하다 느긋해하다, 답답해하다, 끔찍해하다, 서운해하다, 개운해하다, 허전해하다, 짠해하다, 시들해하다, 솔깃해하다, 못마땅해하다, 출출해하다, 흐뭇해하다, 행복해하다, 초초해하다, 착잡해하다, 불안해하다, 애통해하다, 감사해하다 좋아해하다 is grammatically wrong expression. Here 좋아해하다 is used for emphasizing the feeling of 좋아하다. 시 is an honorific particle used for respecting the subject. 어 is an ending suffix used for intimate relation. 안좋아해하다 means "She/He doesn't like it" (She/He is younger than the speaker) 안좋아해하시다 means "She/He doesn't like it" (She/He is older than the speaker) 안좋아해해? means "Doesn't she/he like it?" (She/He is younger than the listener. The listener is younger than the speaker) 안좋아해하셔? means "Doesn't she/he like it?" (She/He is older than the listener. The listener is younger than the speaker) 안좋아해해요? means "Doesn't she/he like it?" (She/He is younger than the listener. The listener is older than the speaker) 안좋아해하셔요? means "Doesn't she/he like it?" (She/He is older than the listener. The listener is older than the speaker)

You are probably talking about "안 좋아하셔?" It's a mix of 반말 and 존댓말 Doesn't he/she like it? where you ask the second person in 반말 while the third person you are refering to is a higher ranked one. (존댓말 is due) example) 어머니도 오셔? - Will mother come, too? (반말 to the person you are talking to) 어머니도 오세요? (존댓말 to the person you are talking to) 동생도 와? : 반말+반말 동생도 와요? : 존댓말+반말 동생분도 오셔?: 반말+존댓말 동생분도 오세요?: 존댓말+존댓말