You are right. "有好多天"="for a couple of days" and "好多天"="a couple of days" In most cases, "有" is a verb which means "have". However here it's a preposition meaning "for". With regard to "好多", when these two characters used together, it's just one word meaning "so many or a couple of", having nothing to do with "good". You can also put similar adjectives after "好", e.g.好大=so big 好美=so beautiful So don't care too much about the literal translation. Well, seems a bit complicated, but it just takes time to totally remember them, I guess. I hope this helps:D