Yes, you are right. Don't forget that you can host unlimited domains with one hosting plan. What you need to do is:
register a domain for your brother via DH panel --> Domains --> Domain Register
You will have a new domain name.
add the domain to your hosting plan via DH panel --> Domains --> Manage Domains --> Add New Domain / Sub-Domain.
You will have your new domain name hosted in DH. I'll suggest you to create a new FTP user for the new domain here so that two users manage two domains separately.
after you have done the above, you will have one more folder /home/newuser/newdomain.com Simply upload the files to this folder and start hosting for your brother.
If you have rewards left in your account, you can also use the rewards to pay for the registration fee of the new domain.
Is that cool?
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