The process works in the following way. We assume that both the systems A and B know the IP address of C.
a) Both A and B send UDP packets to the host C. As the packets pass through their NAT’s, the NAT’s rewrite the source IP address to its globally reachable IP address. It may also rewrite the source port number, in which case UDP hole punching would be almost impossible.
b) C notes the IP address and port of the incoming requests from A and B. Let the port number for A equal X and the port number for B equal Y.
c) C then tells A to send UDP packet to the global IP address of the NAT for B at port Y, and similarly tells B to send UDP packet to the global IP address of the NAT for A at port X.
d) The first packets for both A and B get rejected while entering into each other’s NAT’s. However as the packet passes from the NAT of A to the NAT of B at port Y, NAT A makes note of it and hence punches a hole in its firewall to allow incoming packets from the IP address of the NAT of B, from port Y. The same happens with the NAT of B and it makes a rule to allow incoming packets from the IP address of the NAT of A from port X.
e) Now when A and B send packets to each other, these get accepted and hence a P2P connection is established.