To fix the issue where your iPhone is stuck in headphone mode and not playing audio through the car's speakers, you can try the following troubleshooting steps:
1. Remove the aux cord from your iPhone and car stereo.
2. Restart your iPhone: Press and hold the power button until you see the "slide to power off" option. Slide to power off, wait for a few seconds, then press and hold the power button again until the Apple logo appears.
3. Check the headphone jack on your iPhone for any debris or lint. If you see any, gently clean it using a soft brush or a toothpick.
4. Once your iPhone has restarted, reconnect the aux cord to your iPhone and car stereo.
5. Ensure that the volume on your iPhone is turned up and not muted.
6. Try adjusting the volume while the aux cord is connected to see if the audio starts playing through the car's speakers.
7. If the issue persists, you can try plugging and unplugging the aux cord a few times to see if it helps reset the audio output.
8. If none of the above steps work, you can go to Settings on your iPhone, tap on "Sounds & Haptics" or "Sounds & Haptic Feedback," and disable the "Change with Buttons" option. This will prevent the volume buttons from affecting the audio output mode.
If the problem still persists, it's recommended to contact Apple Support or visit an authorized service center for further assistance, as there may be an underlying hardware issue causing the problem. To contact Apple Support directly, just select the "Support" link on the lower left-hand side of this forum's web page.