1》peter's shoes is under the bed。 哪里错

2》what is does your mother go to work ,by car or by bus? 哪里错

peter's shoes【are】 under the bed
shoes是复数，谓语动词用复数
【How】【does】 your mother go to work ,by car or by bus?
只能有一个助动词，这句中是dose，因为动词是work
另外表示交通工具方式，用how提问
有不会的可以再问我

peter's shoes are under the bed。因为鞋是复数，所以用are How does your mother go to work ,by car or by bus? is是多余的、因为疑问句已经有了does助动词 ；另外，询问的是方式，所以用how“怎么样”

1Peter's shoes are under the bed. 2How does your mother go to work ,by car or by bus?

heavyer改为heavy原形，how后面用原形

is 改为are，shoes是复数，用复数形式