Teenagers’ parents, often busy, can not set aside sufficient time...

Is the 'often busy' part an appositive?

No.

http://www.chompchomp.com/terms/appositive.htm

Doesn't often busy describe parents?

Busy describes parents. But it's an adjective phrase. Appositives are only noun or pronoun phrases.

To determine if "often busy" is an appositive, we can look at the definition of an appositive. An appositive is a noun or pronoun phrase that provides more information about another noun or pronoun in the sentence. In this case, "often busy" is an adjective phrase that describes the parents. Since "often busy" is not a noun or pronoun phrase, it cannot be considered an appositive. Instead, it is an adjective phrase that describes the parents.