Question about ohms

6 ohm speakers and 8 ohm amps are a love match.

I can tell you why, but if just the answer works for you, then you are done! ;-)

Receivers with 6 ohm switches have those switches to enhance their performance on the test bench, not in the listening room.

The average impedance of 6 ohm speakers is in general (yes, there may be a tiny number of exceptions) is 8 ohms or more. Speakers are typically rated in terms of their minimum impedance, while the load that amplifiers see is more like the speaker's average impedance, weighted by the spectral content of the music that they are playing. Also, the constantly-varying nature of music is different enough from steady-state test bench testing conditions (which is what consumer amplifiers are by law based) that it is a far easier test.

Think of it this way. If your power amplifier was a car, test bench conditions are like driving uphill on a very steep grade for 15 minutes to a half hour at a time while pulling a trailer. Music is like driving across a rolling plain, which is rarely flat, but also never steadily uphill. A resistive load is like a heavy trailer, while speakers act more like a light load, on the average.

The OP talked about a 6 ohm switch which is primarily for use on the test bench. Typically, a "6 ohm switch" reduces the voltage applied to the amplifier's output stage so that the amp won't overheat when driving a resistive load on a test bench with a steady-state test signal.

This is true, if all other things are equal, which they almost never are. But for the purposes of this discussion, I would way "Yes, an amp with a 8/6 ohm switch can possibly work harder in the 8 ohm setting because it makes more power supply voltage available to the output stage.

Notice that I said, "can possibly", and not "always does". In the end a given amount of loudness comes from the same current flowing through the speakers regardless of the capabilities of the source (the amplifier).

Because the 8 ohm setting elevates the voltage available to the amp's output stage, it will make it run a little hotter. AFAIK, the difference is on the order of 10% or maybe a little more.

You've probably been educated to think that power amplifiers are delicate little flowers that need care and feeding to work well. In fact modern power amplifiers are like turbocharged cars. If you doddle around town and don't press the gas pedal down very far, they are mild-mannered. If you floorboard them, they have a lot of reserves to pleasure you with. Setting the 8/6 swtich to 8 increases your potential pleasure a bit.

No. The 8/6 ohm switch makes a minor change in the power output capability of the amp, not its gain. The volume control setting for a given amount of loudness will be the same. There's a pretty good chance that you can change this switch setting while the amp is operating and the results will either be a minor switching transient or nothing audible at all. When you go from 6 to 8 there will be a momentary current draw from the AC line to charge the power supply caps to a slightly higher voltage. When you go from 8 to 6 quickly, there should be very little observable difference. Please follow the manufacturer's recommendations about how to use this switch.

What the 8 ohm setting on an 8/6 switch does is let you turn the volume up a bit before the amp starts clipping. Would you hear the difference in a the best possible listening test? Not so much. The switch is there for the benefit of the test bench and conformance to FTC regulations. Call it a "Lawyer's switch". ;-)

Technically, running an 8 Ohm amp with 6 Ohm speakers would cause the amp to draw more current and run a bit hotter. As long as you're not cranking the second zone, I wouldn't worry about the slight mismatch.