Not when the pc from the local network initiates the exchange. How does it distinguish when an external device in a completely different network wants to start communication with our device?
I assume the packet will be addressed to the router's ip address, but how will the router know who the packet belongs to?
It doesn't on it's own... And indeed external hosts cannot generally initiate a connection to a device that is under NAT (the router's Network Address Translation, which is the way the router converts traffic from/to public IP to/from private IP.) Unless you actually specified.
The way to specify that would be by setting up Port Forwarding rules in the router directing traffic (typically those coming to specific ports of the public IP) to the specified local device's private IP (i.e. 122.74.37.25:8000-->192.168.3.45:8000)
(It's worth mentioning - although not really part of the question since those start with the local device's initiation - that there are protocols/settings like UPnP and Port triggering which allow for local devices to dynamically set up Port Forwarding to themselves.)
