Can you wire a 6 speaker car stereo into a 4 channel amplifier?

Yes but you will have to combine four of your speakers into 2 channels. 2 fronts and 4 rears, or 4 fronts and 2 rears.

There's always the option of a 6 channel amp, but be cautious because your head unit may not have 6 preouts, so you will be doing the same as what i previously stated.