好几 + [measure word] + [noun]
好几 + 十 / 百 / 千 + [measure word] + [noun]
好几 + measure word means "quite a few" or "several". 几 alone is a small, neutral "a few"; 好 in front stresses that the number is bigger than you'd think.
With 十, 百 or 千 it makes a rough large number: 好几十 "dozens", 好几百 "several hundred".
几 in a statement is an unremarkable "a few". 好几 adds the speaker's sense that it is a lot.
好几 is never a question. "How many?" is 几 alone.
Like 几, 好几 needs a measure word before the noun.
With a length of time, 好几 + time word goes after the verb: 等了好几天. Some time words, like 天 and 年, need no measure word; 小时 and 月 take 个: 好几个小时, 好几个月.