Why without headphone my speaker sound is not working?

try to right click on the audio icon on the lower right and try to manually change or select the device audio output, may have to update or restore the audio driver. I would head over to the HP forum to get support.

@jemila it is possible that the "switch" inside the headphone jack is stuck. Even when you remove the headphones, your jack my indicate that the headphones are still connected. Sometimes you can loosen this by inserting the headphones and then rapidly removing it. Try that a couple of times. Even a few puffs of compressed air in between those attempts, may loosen this.

Of course, you need to check your settings and your driver according to the OS your computer is using as well.