Well, for having another site, you can't have another x10 subdomain, as you are only allowed to have 1 x10 subdomain. You have 2 alternatives, make a subdomain of your current subdomain, like sub.yoursubdomain.x10hosting.com , this can be done in cPanel from the "Subdomain" icon, in th "Domain" category.
The other alternative is getting a TLD, a top-level domain. If you don't want to pay for one, I recommend using
http://dot.tk - this is a place where you can get a free top-level domain. You could also go with
http://co.cc, but it has restrictions, like that the domain is only 1-year, and it can't contain most English words, because then it's no longer free.
After you got a TLD - Free or not, doesn't matter really, same steps for both - you have to login to the domain registrar and find the DNS settings page. Here, where it asks you for nameservers, you would have to put in:
ns1.x10hosting.com
ns2.x10hosting.com
When you done this, you would have to go into your cPanel, and choose "Addon domains", again under the category "Domains". Here, you would have to put in the domain you just registered, without the http:// and without the www. (so if you registered mydomain.tk, that is what you put in). Then you would have to choose a directory, this is where your files are, or where you want to put your files.
When all this is done, you would need to wait some hours for it to update.