The audio jack works fine, but in Audacity, I plug in my headphones, but the sound still goes through the speakers. I’ve searched for a solution, not finding one
How do I solve this so that when I listen to audacity, I can listen through my headphones?
That sounds like a hardware problem, or maybe a driver problem. If it’s a new computer maybe you can return it or get it repaired.
I assume this is a laptop?
The audio jack works fine,
What does that mean?
Are your headphones regular analog headphones with a 3.5mm phone jack, or are they USB?
I had a similar problem on my Windows 10 PC. I solved it through free open source “AudioSwitch” (https://github.com/sirWest/AudioSwitch), which allows you to “switch between default audio input or output + change volume”.
If when you plug in the headphones you hear sound in the speakers and headphones, this could be a setting in your sound card. Hold Windows key down, press X and choose “Control Panel” then look under “Hardware and Sound” for your sound card’s control panel.
Gale
It’s a Surface 4.
It doesn’t appear to be. If I listen to other programs or audio, sounds go to the earphones. But not with audacity. According to the settings, the jack is working properly.
I’m loathe to download this; what machine do you have?
I don’t think you should need additional software in order to select the audio output.
See: https://www.microsoft.com/surface/en-us/support/hardware-and-drivers/sound-volume-and-speakers?os=windows-10&=undefined
You don’t need it, but setting and resetting the default audio output in Windows 10 as I had to do was hell. It was convoluted and cumbersome. It involved plenty of clicks. It had to be repeated over and over again. With “AudioSwitch” (https://github.com/sirWest/AudioSwitch), it only takes 2 clicks to switch between speakers and headphones, and back if necessary. AudioSwitch is a safe harmless application. If it does not work or does not suit your needs, you can easily uninstall it. It is running fine in Windows 10 x64.
To be fair, the Anniversary Edition of Windows 10 lets you left-click the speaker icon then choose the playback device from a dropdown menu.
Gale
Have you tried changing the playback device to your headphones in Audacity’s Device Toolbar?
Gale
Not on my Windows 10 system with all currently available updates. Not with the Realtek integrated audio that I have.
This is what I am talking about: Quickly Change the Audio Playback Device in Windows 10 Anniversary Update.
Which devices are you choosing between? Realtek cards usually do have an option to play through speakers and headphones at the same time.
Gale
Sorry! My bad! I had never paid any attention to the upward-facing arrow on the right of the current audio playback device. It does give access to a list of all enabled audio playback devices. I am going to uninstall AudioSwitch. 
I tried to download AudioSwitch and it isn’t free. I’m taken to a page to “donate” and as much as I’d love to donate, it’s asking me to pay in Euros. So really, it’s a dead end.
I can select the audio jack til the cows come home, but the sound still comes through the speakers with the headphones plugged in.
The download link is https://github.com/sirWest/AudioSwitch/releases/download/2.1.5.0.1/AudioSwitchSetup.2.1.5.0.exe, and donation is not mandatory. It can easily be skipped by using the appropriate button. However, as Gale Andrews pointed out, you shouldn’t need AudioSwitch in Windows 10. Is “Stereo Mix” enabled as audio source on your system? You might want to take a look at How to Record the Sound Coming From Your PC (Even Without Stereo Mix)
Robert
Moderator note: For security reasons, please do not link directly to executable files. I have replace the link to “AudioSwitchSetup.2.1.5.0.exe” (above) with text. If anyone wants to use the link, they can copy the address into their web browser address bar. Please note that for safety, EVERYTHING downloaded from the Internet should be scanned for malware / viruses. A good on-line malware / virus checker is: https://www.virustotal.com.
As I asked:
Gale