Ok, so here’s what you should try to do. (I went ahead and took my space bar off of my Compaq laptop and it has a similar set up). The two white pieces need to go together. So both of the smaller “caps” need to connect to one of the larger “caps”.
Then you need to reconnect each of these sets to the motherboard, not the space bar. Once you have both sets of caps on the motherboard, you will notice if you lift one side up that it will sort of “scissor” or make an X.
Now comes the tricky part. I used a plastic splunger but you could also use a plastic butter knife or something else that is thin, flat and sturdy. You will need to place the space bar down like it would normally go. Then using the splunger put it underneath one of the sets of caps, slightly lifting it up and then press the space bar into place. You will need to do this on both sides of the space bar, front and back, left and right.
My laptop only had one bar, whereas you have two. It looks like one bar is already connected to the space bar. I would guess that once you have reconnected the caps to the space bar that you would have to reconnect the bottom bar as well.
I hope this is helpful. I tried my best to describe what you need to do. Let me know how it goes. Good luck!