Question

There are only for ways we can deal with the rubbish是不是有问题？书上说we can……是对four ways作定

修饰，但那样的话吧four ways放在句子里不同啊，应该用in which吧？

Answer 1

没有问题
当“ way ”表示“方式、方法”在句中作先行词，后被一个定语从句修饰时，且先行词在定语从句中充当方式状语，引导定语从句可用 that ，也可用 in which ，或什么都不用。
这其实是个省略句，补全了你就感觉通了：
there are only four ways that we can deal with the rubbish （in）
或者：there are only four ways in which we can deal with the rubbish
正常情况下的定语从句是这样的，但是因为这是种特殊的情况，所以这三种方式都行，类似，还有先行词，reason 作原因状语，可省略引导词why ,或that 先行词time ,作时间状语，可省略引导词when或that
如：The reason (why/that) he failed was his laziness.
I don't know the exact time (when/that) the sports meet will take place.

以后见多了，就不会觉得它别扭了

Answer 2

没问题，不过要在four ways后面加that吧

Answer 3

这个没错，way做先行词的时候，引导词可以用that，in which 或是不用引导词也可以

Answer 4

在way, time, moment, direction 等名词后面所接的定语从句中常常省略that, which, in which, when等