In the sentence below,
The danger comes when teens eager to appear popular accept friends that they don’t really know and post too much information thinking that only their friends will see their page.
What is the structure in the "when" clause?
when teens eager to appear popular accept friends that they don’t really know
I mean, how can I treat the words of "popular accept friends"?
Thank you in advance.
You are parsing it incorrectly.
The relevant phrase is not popular accept friends but eager to appear popular.
Look at it this way:
The danger comes when teens eager to appear popular accept friends that they don’t really know and post too much information thinking that only their friends will see their page.
The sentence could be rephrased in a couple of different ways too:
The danger comes when they accept friends that they don’t really know and post too much information thinking that only their friends will see their page.
The danger comes when teens who are eager to appear popular accept friends that they don’t really know and post too much information thinking that only their friends will see their page.
In any case, the subject is teens who are eager to appear popular.
In this construction, this set of teens is in contrast to those teens who are not eager to appear popular. So, you can't just say when teens eager to appear popular accept friends because you would be changing the meaning of the sentence. The eager to appear popular qualification is essential to the sentence.
I think the issue here is the punctuation.
The danger comes when teens, eager to appear popular, accept friends that they don’t really know and post too much information thinking that only their friends will see their page.
I.e. you can remove the following phrase and it should now make more sense:
The danger comes when teens accept friends that they don’t really know and post too much information thinking that only their friends will see their page.
It's a bit weird that you would pull out those three words and as how to parse them. The phrase "eager to appear popular" is an attributive adjective phrase that modifies "teens". "accept" is a verb that has "teens eager to appear popular" as its subject and "friends" as its object. "that they don't really know" is then a subordinate clause that modifies "friends". I don't understand where you got the idea that you can pick three random words in a sentence and ask how to parse them independent of the rest of the sentence.
