Internal Speakers not showing in Output of Sound application
Explanation

If the sound output device is always displayed as 'Headphones' there are usually three explanations for it:


you have headphones plugged in
the tip of a broken headphone jack still sits in the Mac's audio jack
the Mac's audio jack is defective/broken




Possible solution

Please check with a flashlight whether you can see any debris in the audio jack. If debris/dust builds up it may trigger the electrical contact that makes your Mac switch from Internal Speakers to headphones.

Try to gently blow it out or pick it with a tweezer.