There will be many interesting things you'd like to do them.那错了?原因是什么?

them去掉，活着在them前面加个with

them 去掉，
you'd like to do 部分是定语从句，修饰前面的interesting things,
关系代词可以用that 或which，但因为在从句中作do的宾语，可以省略。
这个句子可以拆为两个简单句：
There will be many interesting things.
You'd like to do them.
将其合并时，先将从句中与被修饰词(many interesting things）表示一样意义的词（them）去掉，用关系词替换，本句修饰物，在从句中作宾语，所以用that.which或省略也可以。
所以，原句中的them是多余的。

去掉them
这是个宾语从句
句中神、省略that
that就有them的意思
所以多余啦

去掉them
定语从句前面已经有先行词了~~

There will be many interesting things you'd like to do
把them去掉

you'd like to do你是想说you would like to do吗？这里不应该这样缩写。 另外你使用了宾语从句things是先行词，所以应该去掉them.

这句话主干的正确语序：
you'd like to do mangy intersting things.
再用 them 话就产生了宾语重复了，即 them 和many interesting things 重复了

同上
them去掉
这是个宾语从句,当先行词作从句的宾语时,that/which可去掉
interesting things就是从句的宾语,如果再加上them就重复了
所以去掉

There will be many interesting things you'd like to do.....
them 多余.........此为一宾语从句 interesting things已经是宾语了，后面省略了that，