1.（对）This is the mountain village where I stayed last year.

此句“对”，是因为在定语从句where I stayed last year 中，谓语动词 stayed 是不及物的，也就是说该定语从句不缺主语或宾语，所以不能用关系代词 that 或 which，而应用关系副词；而先行词 village 是表地点的名词，故用关系副词 where。

2.（对）I'll never forget the days when I worked together with you.

此句“对”，同样是因为在定语从句when I worked together with you 中，它既不缺主语也不缺宾语，所以不能用关系代词 that 或 which，而应用关系副词；而先行词 days 是表时间的名词，故用关系副词 when。

3.（错）This is the mountain village where I visited last year.

此句“错”，是因为在定语从句where I visited last year 中，谓语动词 visited 是及物的，但它后面却没有相应的宾语，所以该定语从句要用关系代词 that 或 which 来引导，而不能用关系副词。由于关系代词在此用作宾语，所以也可以省略。

4.（错）I will never forget the days when I spent in the countryside.

此句“错”，是因为在定语从句when I spent in the countryside 中，谓语动词spent是及物的，但它后面却没有相应的宾语，所以该定语从句要用关系代词 that 或 which 来引导，而不能用关系副词。由于关系代词在此用作宾语，所以也可以省略。

5.（对）This is the mountain village (which) I visited last year.

见前面第3题的解释。

6.（对）I'll never forget the days (which) I spent in the countryside.

见前面第4题的解释。