I just started to get involved in bitcoins recently. I was just wondering if it's possible that after I buy some bitcoins on coinbase and then transfer them to armory wallets. Can this be done?
Yes, you can and should transfer your bitcoin to a wallet you control after purchasing them from a web-based wallet. Never leave a substantial amount of your bitcoin on an exchange or a web wallet.
Coinbase is a company that runs both an bitcoin wallet service and an exchange for purchasing and selling bitcoin for USD. Armory is a wallet that you run yourself on your own computer, and therefore store your own private keys. In the case of Armory, it is a deterministic wallet, meaning that it can regenerate all it's private keys from a single seed.
To transfer between wallets, you generate an address on the receiving wallet, and send bitcoin to it from the sending wallet. The process will be different from wallet to wallet, but this is the typical use case of Bitcoin, and you should become comfortable with it regardless of interface.
If you are new, you may want to read some other questions/answers from this site to give you a better understanding of wallet options: