I asked how many English books she had?和I asked her how many

两句都可以,第一句的是泛指的询问,不一定是询问她,也可以是询问别人,还可以理解为asked 后面省略了一个that,她有几本英语书就变成同位语从句.第二句的意思就完全是我问她她有几本英语书,这两个她就是同一个人.