thinks 后面的 by memorizing the words of songs 这个介词短语不是做宾语，而是宾语从句中的主语，原因如下：
(1) 动词 think 后面可以接宾语从句，不能接“宾语 + 动词原形”。
(2) 介词短语可以作主语，但是谓语动词应该用单数第三人称形式，例如：
To Beijing is not very far. 到北京不很远。
From Yanan to Nanniwan was a three-hour ride on horseback. 从延安到南泥湾骑马要走三个小时。
——《薄冰高级英语语法》p.397
所 She thinks by memorizing the words of songs help us learn English. 应该改为：She thinks by memorizing the words of songs can help us learn English. 或者：She thinks by memorizing the words of songs helps us learn English.