沒有問題
當“ way ”表示“方式、方法”在句中作先行詞,后被一個定語從句修飾時,且先行詞在定語從句中充當方式狀語,引導定語從句可用 that ,也可用 in which ,或什么都不用.
這其實是個省略句,補全了你就感覺通了：
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
正常情況下的定語從句是這樣的,但是因為這是種特殊的情況,所以這三種方式都行,類似,還有先行詞,reason 作原因狀語,可省略引導詞why ,或that 先行詞time ,作時間狀語,可省略引導詞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.
以后見多了,就不會覺得它別扭了