"어머니는 자신이 어떻게 그런 교육을 받았는지 다른 개들이 놀라워하고 부러워하는 것을 보길 좋아했다."
Tandem, Kakao Talk, How to Study Korean, 그리고 Korean Class 101에게 무러봤고 아무도 도움을 해줬어요. 그뿐만아니라 Zoom 한국어 교실에 갔고 선생님은 설명하러 너무 어려워하겠다고 했다.
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In this sentence, '-는지' is a suffix that is accompanied with some interrogative words, indicating that the speaker is talking about some interrogative clause, making a guess, or wants to emphasize the clause. Honestly, I think the sentence given is somewhat unclear since I feel like it lacks some essential component, which I can't tell unfortunately. What I can tell is that the suffix '-는지' is usually followed by the word such as '모르다'(not to know), '알다'(to know), '알려주다'(to tell about). I would interpret like below:
My mother liked to watch other being amazed and jealous of her, after bragging about how she was able to get that kind of education.
There are some useful links provided by @user17915 on the comments, click those links to explore more.