Be aware that most games today have a minimum of a Radeon HD3850 or one to two models below.
Most people make the mistake of assuming that because the first number is higher, the card is automatically better. The first digit is just the series (like 3xxx, 4xxx, 5xxx and so on). The following three digits reflect the power of the card. An HD3850 could be superior to a HD6300, it's just that the HD6300 is a newer series, but a weaker card overall. Of course an HD6850 would be far above both.
I don't know the exact stats, so I can't say if a HD6300M would run the game or not... or whether it's inferior to the HD3850 or not...
It may have sugar, it may have everything nice - but if it lacks spice I'm not interested.
If your HD6300M is part of an APU instead of something soldered onto the motherboard you're somewhat better off than someone using a non-APU system. That's not to say it's any great shakes in the grand scheme of things, but AMD's APUs have been getting some pretty good gaming reviews, especially in comparison to Intel's offerings. Even CPUs like the i5-2500k generally get worse gaming performance when reliant on the HD4000 on the CPU.
That said from what I've seen out of AMD's general progression in hardware power versus model numbering a 6300 will probably be about as good as a 5400-5430 which in turn could match a 4500-4550 or 36xx-37xx model. IOW you'll likely be below the minimum, but not so far below that it would be impossible to run the game.
Stop complaining. I could have done this more painfully. - Dryad from Sacred 2.