High amounts of RAM (more than 4GB) is simply a marketing gimmick. With 4GB of RAM costing $16
(and probably less for an OEM like Dell), why not throw in 6GB or more? However, your brother is completely right in saying that the average computer user will not ever need 6GB of RAM in the lifetime of a $750 computer. You could take 2GB (or even 4GB) out of that computer and never know the difference.
The same thing goes for a quad-core CPU, to a lesser extent. Will you be doing a bunch of multimedia editing and encoding? Great, the quad-core CPU will probably save you a little bit of time in those tasks. Other than that, the quad-core will probably be useless for you for at least several years, and by then you will probably be wanting (or needing) a new computer.
So, is this computer a good deal? That depends on what you will be using it for. For basic use, such as web browsing and word processing, this computer has much more than you need.