Final cut pro - Dual Mono dropdown missing

In your screen shot, I don't see a clip in the Timeline selected. And what's in the Inspector is a clip that has no audio. Select a clip in the Timeline, go to the Audio tab of the Inspector, show us that screen shot.

Configure audio channels in Final Cut Pro for Mac - Apple Support

Make sure you have a channel selected not the container. Post a screenshot of what you’re doing.

You synchronize clips in the browser, not the timeline.

Just select the clips you want in the browser, and do one of the following:

1) Control-click one of the clips, and choose Synchronize Clips...

or

2) From the Clip menu, choose Synchronize Clips...

or

3) Press the keyboard shortcut Command-Option-G

Need to see what you’re doing in the Audio insulator and what you have selected there. That’s where you make the change.