This sounds like homework. We tend to encorage people not to provide answers for homework questions. To that end, what do you think? Have you been through the Collections tutorial? Have you looked at the JavaDocs for ArrayList?
(Also, please don't post topic subjects in capital letters)
You might have critiqued the question. A HASH map is a specific implementation of Map. Did he really want you to uses hashes? Or just to come up with your own implementation of Map? You'd have to guess whether he'd be impressed or insulted that you found the question ambiguous.
The latter is pretty easy ... a map has a bunch of keys and a bunch of values. Look at the Map API. Could you write those methods using lists to store keys and values?
A good question is never answered. It is not a bolt to be tightened into place but a seed to be planted and to bear more seed toward the hope of greening the landscape of the idea. John Ciardi