If I delete my old Apple account can I keep the new one since the old one was hacked

It should only delete the old one. You have to be able to sign in to your old Apple ID account page on a Mac, PC, iPhone, or iPad.  Be sure to read the "Before you request deletion of your Apple ID" and "After you request deletion of your Apple ID" sections in:

How to delete your Apple ID account - Apple Support

Be aware that when your Apple ID account is deleted, your account details and the data associated with your Apple ID are permanently deleted from Apple’s servers. You (or anybody else) can never sign in to that account again, and you won’t be able to access any data, content, or services that were associated with that Apple ID.

It should only delete one account. They are two separate accounts.

All purchases made using an Apple ID are tied to the ID. Delete the ID and you will need to download them using your new ID. There have been posts by people who have contacted Apple Support and they were told that if you delete an ID associated with an email address, you can never reuse the email address for an Apple ID.   Make sure you sign out from the places in the 4th link before deleting the ID.

How to delete your Apple ID account.         

Apple ID – How to Delete.        

Delete Apple ID (new).         

What to do after you change your Apple ID or password - Apple Support