This is The Simple Game System, a role-playing game of supreme simplicity, ease of play, and fast action. TSGS uses ordinary six-sided dice to resolve actions, and requires only the most basic of arithmetic, making it suitable for players of age 10 and over and having any level of RPG playing experience; however, as is always true, really simple games need experienced game masters. The simple mechanics of TSGS also make it very suitable for online use, whether via virtual tabletop, play-by-post, or any other method you might imagine.
This is something I've been looking for as a DM/GM with kids (I've been trying to even develop my own, with no luck as to what systems to work with.). It's simple enough that teaching the game should not be too difficult, while complex enough to allow for interesting character dynamics and decisions for more experienced gamers.
If you're looking for a new game system to try out, I couldn't recommend this one more!