[译] 双方都坚持按自己的方法做这件事。
[误] Each side stuck to do it their own way.

[正] Each side insisted on doing it their own way.
[注] “坚持要做某事”，英文常用“insist on doing something”；“stick to”也有“坚持”的意思，但常接表示“观点”、“立场”的名词，“to”是介词。