Here are the specifics:

HP pavilion G6 2011eu

DISPLAY 15,6"(39,6CM) 1366 X 768 CPU
INTEL® CORE™ I5-3210M 3M 3.10 GHZ, RPGA
RAM 6 GB DDR3
HDD 1 TB SATA
DVD SUPERMULTI 8X DVD±R/RW
VIDEO AMD RADEON HD 7670M 2GB

Definitely it will. Your specifics are way above what is recommended for the game.
My computer's only got 4GH RAM and a 1BG video card, and the Witcher 2 was running perfectly.

You sure about that? The first digit for AMD cards is the generation, so the second digit is the most important one. Recommended is a 3850, emphasis on the eight, and keep in mind that we're talking about a 7670M, not a desktop one. There are a lot of factors at play with graphic cards, enough to where this isn't a "2 GB is better than 1 GB in all cases" situation.

Going to go ahead and say that it might run, but whether or not it'll do so "properly" without some concessions in eye candy (and perhaps even a lower resolution) is up in the air. I don't know enough about the mobile cards to say for sure, only that they're less powerful than their desktop equivalents and a desktop 7670 isn't exactly ideal for this game.