What am I doing wrong? Can't play from Macbook air to home speakers

If you haven't already, try this --

Click on the Apple logo at the top left corner of the Macbook Air screen and choose "System Preferences", the second item in the drop-down menu. 

In the System Preferences window click on the "Sound" icon, it's the fourth from the left in the top row of the second group of icons. Click on the name of the device you have connected to the Macbook's USB or 1/8" audio output. Test for sound.

I did try that before. That did not work. No device showed up, whether digital or analog.

I have a Macbook Air and just tried analog output to an external powered speaker connected through the 1/8" headphone jack . The external speaker shows up and worked fine when selected.

Then I tried output from one of the two USB C ports on the Macbook Air to a Pro-Ject Pre Box S2 Digital DAC in my office system. The DAC shows up in the Sound Output preferences window and plays fine through my office system. 

Could it be the mixer that is the problem?