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There is a practical answer as well as a technical answer to the question. See below for a precise technical comment on output impedances.
Amplifier manufacturers quote a minimum load resistance or impedance that should be used with an amplifier. Most good quality amplifiers will handle a 4 or even a 2 ohm load without any complaint. In these cases, amplifiers are rated to deliver a certain amount of power into an 8 ohm load but this does not specify that 8 ohms is the minimum load that can be used.
If the amplifier is rated to drive 8 ohm speakers, using 6 or 4 ohm speakers will tend to draw more current than with an 8 ohm speaker if all other factors are the same. This can lead to increased distortion or as power levels increase can result in damage to components. In most cases, using a 6 ohm speaker on an amplifier rated at 8 ohms will work without any problems because manufacturers provide a margin for safety. It is wise to avoid using the amplifier at high output levels and even wiser to consult the manufacturer before doing it. Damage is very unlikely, but possible.
The technical details of amplifier impedances There is no "8 ohm amplifier" at all on the market. All amplifiers have an output impedance less than 0.5 ohms.
The amplifier will have an output impedance of around 0.05 ohms. In hi-fi we have always impedance bridging. Zout << Zin. That means the output impedance of the amplifier is much less than the input impedance of the loud speaker.
The damping factor Df = Zin / Zout tells you what Zout is.
Zout = Zin/Df.
If the damping factor Df = 200 and the loudspeaker impedance is Zin = 8 ohms, the output impedance of the amplifier is Zout = 8 / 200 = 0.04 ohms.
See the related link and look at "Voltage Bridging - Zout < Zin".
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