hi i have macbook pro 2016 and i don't see built-in speakers as an option in the Output window,

This can be hardware failure. Please reboot your Mac first to see if the issues persist.

After that, and the issue persist, boot It in the safe mode

Start up your Intel-based Mac in safe mode

1. Turn on or restart your Mac, then immediately press and hold the Shift key until you see the login window.
2. Log in to your Mac.
3. You might be asked to log in again.
4. On either the first or second login window, you should see “Safe Boot” in the menu bar.

If booted in safe mode, try these steps

Check your sound settings

First, disconnect any cables from the USB, Thunderbolt, or 3.5mm audio ports on your Mac.

1. From the Apple menu , choose System Settings (or System Preferences).
2. Click Sound.
3. Click the Output tab, then select the built-in speakers. If you don’t see built-in speakers as an option in the Output window, contact Apple Support.
4. If the Output volume slider is set low, move the slider to the right and test again.
5. If the Mute checkbox is selected, deselect it and test again.
6. If you still don’t hear any sound, contact Apple Support.

Hope this helps!

when ever I see "Headphones" in my output tab, it means my headphones are plugged in. if your headphones are connected to your Mac, unplug them and "headphones" should revert to "built-in speakers".