She knew that her mother would know from the way the wall
had paper been painted that no adult had done it.

それと、

She knew when she said that her daughter could
tell a truth that she was exaggerating a good deal.

この2つの文、構造は同じです。
パッと見た目には分かりにくいのです。
一瞬、あれ、と思う人が多いのではないでしょうか？

She knew that her mother would know (from the way the wall
had paper been painted) that no adult had done it.


She knew (when she said that her daughter could
tell a truth) that she was exaggerating a good deal.
としてやれば、なんてことはない文章です。
knowの目的節となるthat 節が離れていると分かりにくく
なるのです。

こんな英文書かないで！　といっても仕方がないのですね。
入試問題ですから。