There are a lot of factors in this, so bear with me trying to summarise and also painting with a very broad brush so as not to get too tied in knots with the details.
If you have all 6 Ohm speakers then, if the amp.features an impedance switch, you have a choice. You can play it safe by setting the amp to 6 Ohms. This will introduce a current limiter to stop the speakers drawing too much current if you're a bit enthusiastic with the volume control.
Alternatively you can leave the amp on 8 Ohm, and then just exercise a bit of caution soap not to go OTT with the sound level.
The physics here is about how amps drive speakers and what speakers do in response.
An amp is a voltage raising device. When you turn the volume dial the amp responses by creating a progressively larger modulated voltage signal across the speaker terminals. The speaker cone responds by moving (it's a wire coil in a magnetic field), and moving that wire in the field causes a current to flow. The speaker is sucking power from the amp in order to do some work. The amp responds by supplying that current.
The lower the Ohms rating then the more current is required to do the same amount of work.
Amps blow up when the speaker tries to suck more current than the transistor pair and power rails can supply.
Setting the amp to 6 Ohms puts a ceiling on how much current the speakers can suck, but its not as simple as that.
Every speaker goes through an impedance range relative to frequency. Its like a roller coaster of a curve where the Impedance dips and peaks at various frequencies. An 8 Ohm speaker might be 3-4 Ohms at some frequencies, and 20 Ohms or more at other frequencies. At high Ohms everyone is safe, but at lower Ohms values - the closer the speaker gets to looking like a short with no resistance at all - then the more risky it is for the amp.
To add to this, there's the phase angle of a speaker. This also changes with frequency, and it has the effect of making the amp see a bigger load that sucks even more current.
Fortunately music and movie sound tracks play a broad range of frequencies all at the same time, so the peaks and dips are sort of evened out to a degree.
Here's how this relates back to a 6 Ohm limit.
Setting the artificial limit also has the effect of limiting the power during brief peaks in the audio for say a gun shot or ka-boom moment. In themselves they're not a risk to blowing the amp because the demand is momentary. The amp has time to recover. The transistors aren't undergoing lots of heat stress as say they might with a long sustained music note at just the wrong frequency. The amp can't decide when it should and shouldn't apply the limiter though, so everything gets cut above a certain current limit.
