" She asked her sister (that) why she had gone there when she knew she wasn't there. We do not use "why" and "that" together. This is a subordinate clause: when she knew she wasn't there.
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LaboriousShe said to her sister, "Why did you come here when you knew I wasn't here?"She (Jane) asked her sister (Lois) why she (Lois) had come there when she (Lois) knew that she (Jane) wasn't there.