"I have a very long banana."
Translation:저는 아주 긴 바나나를 가지고 있습니다.
In my experience it would be more natural (and easier) to just say 난 긴 바나나가 있어
있다 is an intransitive verb, meaning it does not take an object, so using the particle 를/을 is impossible. This is because the verb literally means "to exist". "저는 아주 긴 바나나가 있습니다" would be correct because the banana takes the subject particle 가, such that the sentence literally translates as "As for me, a very long banana exists." The thing possessed is the subject that does the existing.