"Barış's mother liked my glasses a lot."
Translation:Gözlüklerim Barış'ın annesinin çok hoşuna gitti.
Hoşuna gitmek is a verb that is usually used with 3rd person (just like gustar in Spanish) It just means 'to like'.
Literally: My glasses went to the liking of Barış's mother a lot.
Usage note: Prefer this over sevmek, beğenmek and hoşlanmak for only specific objects and activities. Not with humans nor general activities/concepts.
Yes, that's quite important! The word hoş (which actually means nice and is never used as a noun but here it means pleasure) first takes personal possession endings (my, your,..) and then dative ending (to) in order to mean to my pleasure, to your pleasure, etc..
Hoşuma gidiyor - I like it.
Hoşuna gidiyor. - You like it.
Hoşuna gidiyor. - He/she likes it.
Hoşumuza gidiyor. - We like it.
Hoşunuza gidiyor. - You like it.
Hoşuna/Hoşlarına gidiyor. - They like it