請問句子中為什麼要用knowing,是因為分詞構句嗎? 那如果用parents who knows的句型可以嗎? 感謝 They are able to contact drug dealers without their parents knowing about it.?

without 是個介系詞，後須接名詞或名詞面語。
(without 的用法可見，http://dictionary.cambridge.org/dictionary/english-chinese-traditional/without)

I couldn't have done it without you.
You shouldn't drive for more than three hours without taking a break.

注意到without 之後，不可直接使用動詞，而必須是動名詞。

原句可改寫成
They are able to contact drug dealers without their parents knowing about it.
= They are able to contact drug dealers without their parents' knowledge.
= They are able to contact drug dealers in the absence of their parents knowing about it.
= They are able to contact drug dealers with their parents knowing nothing about it.

如果採用子句寫法也可以
They are able to contact drug dealers (under the circumstances) that their parents know nothing about it.

They are able to contact drug dealers without their parents' knowing about it.
你好像漏打了一個表示所有格的記號在parents後面。
knowing是「動名詞」，當作介系詞without的受詞。
without their parents' knowing about it是「介系詞片語」，用來修飾不定詞片語to contact drug dealers，表示條件。是副詞性質的「修飾語」。

我覺得正確句子應為They are able to contact drug dealers without their parents' knowing about it.
理由是that名詞子句不能接在介係詞without後
,所以必須把主詞改成所有格而動詞改為動名詞

They are not able to contact drug dealer without their parents knowing about it. As you know that in this sentence. "without" is a preposition and "without their parents knowing about it" is a prepositional phrase and to modify " to contact drug dealer". Yip