You can work out this problem (in) this way.Let me explain it (in) another way.表示行为方式的way前面的介词in美国人口语习惯上省略.所以说this way名词短语作宾语但相当于作状语而不是通过介词短语作状语.所以说引导way的关系词可以是关系副词where(实际上不用)也可以是关系代词that但不用which,或用in which当然也可以省略.例如：I don't like the way (that/in whinch）he speakes to his mother.
the reason和the way一样只不过省略for,但可以用关系副词why来引导.这都是美国人的习惯问题,没有为什么,可以在网上搜关于省略句的文章.