The Model 24 has several output paths. AUX OUTPUT is the typical monitor connection. But depending on your setup you could also use the MAIN OUTUPT or the CONTROL ROOM for your amplifier. Be just aware that typical mixer outputs are loud compared to hifi equipment connections (+4 dB vs -10 dB), if you go to a regular hifi amplifier. But not really a problem.
Additionaly the MAIN OUTPUTs provides a balanced connection, if you have need for it.
Make sure to avoid using the Phono inputs though. They’re designed for weaker signals and if you connect the mixer to these you will most likely end up with a distorted sound.
You're probably not going to like the results of using a home stereo system for recording monitoring though. Home stereos are so colored you won't have any idea what you are really recording without some other way of verifying it. You should at least turn off the "loudness" control and set all the EQ flat, if possible. Then there is speaker coloration to consider.