这题是考定语从句的连接词.定语从句修饰days,而且days在定语从句中做spent的宾语,即把定语从句单独拎出来说完整是I spent the days with Mrs Brown,因此该连接词要用that/which或者不填（因为作宾语,连接词可以省略不填）.
但是,如果days在定语从句中做时间状语的话,就要用when来做连接词了,如：
I'll never forget the days when I lived in the countryside.