As long as the speakers ohms are higher than the amps ohms are as much as the watts are higher the sound get's better/deeper/more power. In reverse the amp needs to deliver more which it quickly can't, with lack power in the actual sound. The 6 ohm you've mentioned are mostly (if not always) designed next to 6 ohm amps.
I may not be a music business technical, but i've done my lessons on electronics in school with good results. And those same calculations made me blow away my friends. And i can tell you that the levels and sounds we reached, and the differences between in the cars were perfectly to be heard (and to be seen at the car's body and accessories )
Start calculate with the ohms, watts, voltages and amperes and you can no other than say i'm right. (or let a specialist calculate for you)
In this case, as i said no different, the 4ohm speakers on the 6 ohm amp can go perfectly right if the amp feeds enough watts (at least about 1,5 times the speakers need), which in many cases is not.