You cannot delete your only inbox. If you just have one inbox, you will need to create a second inbox, even if it's just using a fake name and email address.
Once you have more than one mailbox, go into the Settings → Channels and select the mailbox you want to delete and click the trash can icon.
A window will open and ask for confirmation to delete.
⚠️Caution! Before you delete anything, make sure you don't need any of the tickets in your mailbox, because once deleted all of the tickets in the mailbox will be removed as well.