The big problem here is that it look like the rated sensitivity of these speakers is 86 dB SPL (under normal test conditions--1 kHz, 1 watt, measured at one meter on axis in a standardized size of room). That's not the lowest sensitivity rating I've ever seen (by quite a stretch), but it's definitely on the low side.
So, depending on how loud your idea of "decent level of sound" actually is, and to some extent, how large and reflective of a room you're planning to install them in, there's a decent chance you may end up disappointed.
A lot here depends on your listening habits though. If you're planning on listening to something like hard rock or heavy metal, I foresee pretty serious disappointment in this combination. There's simply no way you're going to get the volume levels most people want for that kind of music.
Even with a more powerful amplifier, these just aren't the speakers for that kind of music. They won't play very loud, and they won't produce deep bass.
On the other hand, if you mostly listen to jazz or classical, and especially if you want it primarily as background music at fairly low volume so you can carry on a conversation without it intruding...they may work out really well.
As far as the impedance mismatch (amp rated for 8 ohms, speakers rated at 6) it's quite unlikely to be a major issue. The impedance of a typical loudspeaker varies pretty widely with frequency at best, and the difference between 6 and 8 ohm nominal impedance is actually fairly small. Again, it's going to come back to listening habits though. If you're running the amp right to the ragged edge, the reduced impedance could lead to a problem--but you don't have to reduce volume much to reduce that substantially.
The preceding is largely addressing the specific speakers mentioned here. It kind of hints at the situation, but doesn't really directly address using a small amplifier to drive large speakers.
To state the situation directly, the size of the speakers doesn't matter nearly as much as their sensitivity. Just for example, if I connected the same 10 watt per channel amplifier to (much larger) Klipschorn loudspeakers, the situation would be drastically different. It would have no difficulty at all producing what most people would think of as loud music--even thunderously loud music with quite deep bass. The difference is that Klipschorns have a rated sensitivity of 105 dB SPL for one watt of input (again, 1 kHz, one meter, in a standard sized room). They're sensitive enough that you don't need to feed them a whole lot of power to get a lot of output.
And as a horribly over-simplified rule of thumb, speakers that are physically larger will tend to have higher sensitivity. So, the combination of a small amplifier with large speakers is definitely not destined to end in tears. In fact, a lot of the problem here is that the speakers he was asking about honestly aren't particularly huge. The same amplifier with larger speakers that had a higher sensitivity rating could easily work out quite a bit better.
This combination is not going to play very loud. It mostly comes down to two questions: what kind of music do you listen to, and how loud do you want it? If you want loud music with deep bass, you'll almost certainly be disappointed. If you want "soft" music at fairly low volume, it's likely to work out a lot better.
But a different amplifier would/will only mitigate that to a fairly limited degree. Regardless of the amplifier you use, these speakers simply aren't every doing to produce really loud music or (especially) deep bass. Just not going to happen.