A collision domain is an area where collisions can occur. This happens when a network device does not route data, but just sends it everywhere.
Switches, routers and bridges break collision domains. Hubs on the other hand, don't.
In the first image, the two hubs at the top are divided by a bridge, so would make up 2 collision domains. The two on the bottom don't, so they are in 1 collision domain. So 2 at the top, 2 to the right and 1 at the bottom. 2 + 2 + 1 = 5 collision domains.
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In the second image, the three systems on the switch are broken into three collision domains. The set to the right of the router are connected through a hub, which is 1 collision domain. The set on the bottom is divided by a bridge only. So these make up 2. So 3 + 1 + 2 = 6 collision domains.
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Broadcast domains on the other hand can only be broken by routers, because of the Layer 3 addressing.