how do I hook up my galaxy prime core to a car stereo

If you want to connect it via USB, you will only be able to use it as a 'memory stick', so your stereo will only read MP3 (or valid format) files off of it to play, not play audio directly from the device.

Now, for that to work, your device must be in 'Mass Media Storage' Mode, and sadly, that was long removed from Android; chances are that the version you have on your phone no longer has it, but if you do, an USB Mode notification should pop up when you connect the device to the stereo or to a PC.

Some car stereos support MTP Mode as well, but those are rare as many are moving to BT connections now.