It’s the Hong Kong people who first used “拜拜” [bai bai] to represent/transliterate “Bye bye” in English and then introduced it to the Mainland. Taiwanese people chose the different character “掰掰”[bai bai].
No matter which character you wanna use, we could find “手” [shou 3] (hand) and its variant in both “拜” and “掰”.
“拜” means the greeting/respect gesture that Chinese people make a fist with their one hand and hold it in the palm of the other. You could bow with this hand gesture, which is also a “拜” but too formal for daily life. Namaste is another “拜” to ask, worship and pray, as Buddhism has been popular since the Han Dynasty （AD 64）. If the movement goes more exaggeratedly, you could drop to the floor and knock your forehead on it to demonstrate “kowtowing”. That’s a kind of “拜” only in temples, super solemn ceremonies and tv drama.
“掰” means breaking off things with hands. So there is a “分” [fen 1] (separate/part) inside the two hands. “分” is composed by a “刀” [dao 1] (knife, machete), splitting the stroke above into two. And “分 手”[fen 1, shou3] (let go of hands) means to break up in a relationship.
Both of them fit in the context to some extent. And being loanwords, they are less formal than “再见”[zai 4, jian 4]（again， see #you# = goodbye）and “告辞”[gao 4, ci 2] (deliver， farewell speech= goodbye).
Turns out its a sort of hybrid slang word, which I guess duolingo maybe put in as an interesting wildcard to break from the monotony of the rest of this lesson (explanation of bai bai: https://www.quora.com/How-do-you-say-see-you-later-in-Mandarin-Chinese)
Also, it doesn't match the 'correct' answer, as shown at the to of this page! It's an ERROR.
Probably correctly intruded in a different lesson.
DuoLingo doen't fix errors in Chinese or Japanese courses. English is their money maker. Everything else, they get a user base, but don't fix errors.
People do or because of errors, but their is always a new user to replace that one. Add and subscription revenue isn't affected. So they just debut a language m and collect money. No ITERATION like real teachers. No BUG fixes either.
the answer it accepts is 拜拜 (bai bai) which is taken from English Bye Bye. Both 再见 and 拜拜 are things you could say when parting company just like in English Goodbye and Bye bye. the question should be corrected to ask for bye bye or goodbye specifically making a distinction since there are two different phrases.
Ultimately it is your choice. However, this course teaches the simplified version, so some traditional options may not be accepted even though they are correct, so it would be preferrable to use the simplified version.
The simplified version is also easier since it was reportedly 'created' to improve literacy rate. Many words, especially those that are not too complicated, are carried forward from the older version while many others are quickly recognizable. It is also, arguably, more useful in this day and age.
The advantages of the traditional version is that it is much easier to 'learn' the simplified version, having known the traditional, than vice versa; Japanese kanji follows the traditional version. Some characters were merged to one simplified character, so some history there may be lost. Since it retains the original features of the characters, it is used to show the evolution of these characters through the passage of time, and to know the reason why a character is so "assembled".
I'm feeling generous.. everyone who has commented on this post who knows English, German, Spanish and Chinese will receive a lingot. Starting 21Feb2020. You don't have to be fluent by any means, "learning a language is a life choice, not a goal." That being said congrats to those who choose to expand their true vocabulary. *I will always reward those who are deserving.