Final Cut Pro clips don't play in preview browser

I've labeled your screenshot so we're all on the same page linguistically.

First thing I see is that your Timeline pane is NOT active, because the clip selection highlights are in white, not yellow. So no, the space bar isn't' going to do anything.

Before we go any further, try this:

1- Click once inside of the Timeline Viewer and hit Shift-Z.

2- Go to the Window menu, to Workspaces, click on Default.

3- Hit Cmd-2, then hit the space bar, what happens?

If that doesn't work, then do a screenshot AFTER doing all of that.

It is unclear what exactly you are saying, because your screenshot does not show your clips in the browser.

The browser is that section at the top left. It is currently showing Titles and Generators.

If your problem is that you can't see your clips, then just click here: