Lower ohms is a harder load for an amplifier because it requires more current for the same amount of power. Current is difficult, voltage isn't.
In all likelihood, you won't notice any problem driving 6 ohm speakers with an amp that is advertised for 8 ohm speakers. Especially at lower volumes.
If an amplifier does have a problem driving low ohm speakers, it may automatically shut down or the sound will start to fall apart and become a little messy. If it really can't handle it, like an amp trying to drive 1 ohm, and there is no protection built into the amp, then something may get damaged in the amp.