Who are teenagers? They are young people who are from thirteen to nineteen. Look at the words such as thirteen, fourteen....nineteen. They all have teen, so people who are from thirteen to nineteen are called teenagers.

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Is this explanation grammatical? Would you let me know any ungrammatical expressions?

The only thing I'd modify is this:

They all have the suffix -teen, so...

=)

Yes, the explanation provided is grammatically correct. There are no ungrammatical expressions in the given explanation.