If you look at Ohm's law, it explains a lot. V (Volts)= R (Resistance) x I (Current). The Ohms is resistance and if it drops, current increases. Since Voltage stays the same the variables are Resistance and Current. The problem many amps have is with more current you have more heat. Amps are usually designed to match the resistance (or impedance) to maximize efficiency. It cost more to design an amp that can handle lower impedance speakers. In the real world, most speakers dip to 4 ohms or so in certain frequency ranges (even though they are rated at 8 ohms). I cannot think of a single consumer AVR that cannot handle a 6 ohm load. In reality many can handle 4 ohm loads under normal listening conditions.
I would be completely blown away if your amp couldn't handle a 6 ohm load. Many in here have used cheap AVRs to power 4 ohm speakers with success for many years. Speakers are not a set impedance. With each frequency the load to the amp changes. A speaker's resistance is an average given by the speaker manufacturer and is not a simple number that tells all. I think this is why people think a certain amp is better than a different amp. It just performs better with a certain speakers impedance curve.