So brave was she that she faced the difficulty she had _ her
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A, difficulty in doing sth, 这里的IN可以省略,分析一下句子可以知道she faced the difficulty stuying her English是主句,这里she had是用来修饰difficulty的,如果选studied的话,就出现了两个主句,she faced the difficulty和she had studied her English, 且两个句子之间没有AND 连接,所以是不对的,故而应该选择studying