Will the program file generated for c8 device work on c6 device?

As the come out of the FAB, the devices all run at slightly different speeds, and get "binned" as different devices. In the software, these bins are modeled as speed grades. They are modeled between two operating conditions, the fast model, which is the fastest a device will run(and accounts not just for the fastest Process out of the FAB, but the fastest Voltage and Temperature operating conditions within spec, which is just PVT). The fast model is common across all speed grades. The other model, the slow model, varies across speed grade, getting slower with the higher number. Note that it's possible that as the process gets better, the FAB may produce more and more of the faster parts, but if there is demand for slower parts, they can be marked as slower parts and shipped that way. The speed grade just means that's the slowest they could be, but they could be faster. So yes, it should be fine in the faster speed grade, but if you meet timing in the slower speed grade, you might as well buy the cheaper part.