Depending on what he is doing. If he want to multitask a lot then 6gb of ram is useful. On my laptop, I have a Phenom II x4 N930 2GHZ with 6gb of ram and I sometimes run out of ram when I try to play games at the same time I have chrome open with 50ish tabs. With chrome pegged at 33 tabs now and minimal background stuff, I hit about 3.4gb of ram usage. Even gaming can benefit as some games can use up to 4gb of ram and not leave enough for background and OS.
It may be better off to save up for a whole new build though as the Phenom is quite old for gaming.