You must tell duckdns what your current external IP address is. Best would be that your home router contains a client that does this automatically. Next best is to run a client on a machine on the home network, probably the machine running your content server, that watches for an IP change and notifies duckdns.
You must also setup port forwarding on your home router so that the internet can see your calibre server. Exactly how you do that depends on your router. It is best that the machine running the content server have a fixed IP address on your home network.
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