The house in which we live is very large.

This is the reference book of which the teacher is speaking.

改写为：

(1) The house that we live is very large.(错误的，live 后需要加介词in）

(2) The house that we live in is very large(正确）

(3) The house we live in is very large(正确）

(4) This is the reference book that the teacher is speaking of.（正确）

具体回答如下：

(1) 以上第1个句子改写不正确，因为关系代词that一般引导定语从句要在定语从句作主语，宾语，表语等成分，你改写定语从句却做了地点状语，正确改写应该为用关系副词

The house in which we live is very large.

=The house where we live is very large

=The house that we live in is very large （介词放在句末，可以用关系代词that）

=The house we live in is very large.

(2)改写的第2/3/4句子属于正确的句子把介词紧跟动词后，是可以这样改写的，还可以省略关系代词，如果提前只能用关系代词which引导定语从句，

This is the reference book that the teacher is speaking of 

（如果介词在句末，可以用关系代词that也可以省略）

=This is the reference book of which the teacher is speaking.

（直接放在介词后充当介词宾语的关系代词只能用which)

=The is the reference book the teacher is speaking of.

（关系代词在定语从句充当宾语可以省略） （speak of 属于动词+介词=构成短语动词）

以上3种表达都正确

(在定语从句中，介词提前用关系代词which/whom,指物用which,指人用whom,介词移后，可以用关系代词that，甚至还可以省略充当宾语的关系代词that/which）

(3)要注意这种表达the +名词+of which=of which +the 名词=关系代词whose +名词引导定语从句，在从句作定语成分

例如：

I saw a house whose roof is red 

=I saw a house the roof of which is red.

=I saw a house of which the roof is red

特别备注that 还可以在从句充当方式状语，先行词必须是the way。例如：

I don’t like the way that you talk to me.

I don’t like the way in which you talk to me.

I don’t like the way you talk to me.

上面3种表达都是正确的。