这个英语语法填空该怎样填？

Question

she saw an advertisement recruiting（征募） host families for foreign students, and that was __1___ Carey (from Chicago, US) came to her home. Carey is actually not a student, but a manager. She stays in Li's apartment for free， __2___ has to teach Li oral English for 1 hour every day. “She could hardly speak Chinese at the beginning, and __3___ had to guess what each other meant through gestures, ”said Li.
Two months later, they could talk to each other __4___ gesticulating（做手势）. Now, Li can communicate with any English-speaking person freely. About one hundred Shanghai families have received foreign boarding students, and the figure is rising .

答案是：1.how 2.but 3.we 4.without 我需要解释为什么这个答案！谢谢！

Answer 1

1HOW 是问CAREY怎么样回到她自己的家。
2BUT是连词连接2个句子，因为前面已经有STAYS这个动词了，后面HAS是动词谓语形式，同一个句子不可能有两个动词做谓语。句子意思刚好表达转折的意思所以用BUT。
3 HAD前面却主语 主语一般都是用WE.表达。
4 WITHOUT是介词后面用动词的ING形式表伴随。追问

第一个how能给我详细的解释吗？联系上下文...谢谢！

追答

前面她看到一个广告招聘(征募)为外国学生寄宿家庭,，然后AND THAT的THAT就是指代前面的句子。
That was HOW Carey (from Chicago, US) came to her home.

因为HOW 引导一个表语从句。引导词有how how充当方式状语 when充当时间状语 what充当直接宾语 who充当主语where充当地点状语 why充当原因状语whether充当选择性状语引导主语从句和表语从句的引导词有 who，whom，whose，that，which，when,where,why 等
句子意思是问Carey (from Chicago, US) came to her home.来到她的房子。前面句子意思明显说明了她是通过看到广告招聘才来到她的房子，就是通过这一种方式。所以答案是HOW

Answer 2

1.how 怎样，这就是Carey怎样来到她家的。

2.转折，她免费住在Li家里，但是每天要教Li一个小时的口语
3.我们要通过对方的手势来猜对方讲什么
4.without除了。前面说通过手势来猜意思，但是两个月后他们可以不用手势来对话。追问

第一个how能给我详细的解释吗？联系上下文...谢谢！

追答

我读起来是挺顺的.有种只能意会的feel 不过可能是我功夫不到家哈哈
应该可以改成这样的，Carey (from Chicago, US) came to her home by seeing an advertisement recruiting（征募） host families for foreign students.
Carey通过看到应征广告的方法来到她家里。

Answer 3

me to her home. Carey is actually not a student, but a manager. She stays in Li's apartment for free， __2___ has to teach Li oral English for 1 hour every day. “She could hardly speak Chinese at the beginning, and __3___ had to guess what each other meant through gestures, ”said Li.
Two months later, they could talk to each oth