正确的是：Not knowing how to do it,he went to her for help.
如果用don't know how to do的话,句子有明显的语法错误,因为don't know 和 went to 都是谓语,而一个句子中不能有两个谓语,所以必须把don't know改为非谓语的形式:not knowing.
如果一定要用don't know的话,句子可以是这样:
He doesn't know how to do it,so he went to her for help.
用一个so 或者 and 等连接词来连接两个完整的句子.