This post is regarding the ARP process in which PC A is trying to ping PC X on a different network, also referred to as Proxy ARP, e.g

PC A -> [Router 1] -> .. -> [Router N] -> PC X

I've tried to talk to my ccna teacher about the process and etc but she only confuses me more, and the CCNA textbook doesn't really touch on the subject that much besides just a regular ARP request. So far regarding this I've come up with the following,

• The ping command is issued to PC X’s IP address. In order for PC A to successfully send the packet to PC X it must send to its default gateway.
• PC A checks its ARP cache/table to see if the default gateways corresponding MAC address exists.
• The MAC address does not exist so a broadcast ARP request is sent. The London (Cisco) router recognizes the ARP request for PC X’s network and sends PC A its own MAC address  as an ARP reply.
• PC A receives the default gateways MAC address and enters it into the ARP cache and forwards the packet to the London (Cisco) router.
• The London (Cisco) router forwards the packet to the Toronto (Cisco) router because it is the next hop in its routing table for the network PC X belongs to.
• Toronto (Cisco) router then forwards the packet to PC X.

My teacher says this is wrong, but I'm not certain on what is wrong or missing, If someone could enlighten me, that would be greatly appreciated.

ARP is only used on local network segment.  Proxy ARP is used to permit physical address routing between network segments on the same LAN.  You generally don't see it being used which is probably why your book didn't focus heavily on it.

[quote author=Lord[nK] link=topic=14858.msg151391#msg151391 date=1146180216]
ARP is only used on local network segment.  Proxy ARP is used to permit physical address routing between network segments on the same LAN.  You generally don't see it being used which is probably why your book didn't focus heavily on it.
[/quote]

Besides the fact, we still need to understand it.

Just to follow up,

• To reach Host X, Host A needs the MAC address of Host X.
• Therefore, Host A broadcasts an ARP request on Subnet A
• Host is requesting that Host X send its MAC address
• The ARP request packet is then encapsulated in an Ethernet frame with Host A's MAC address as the source address and a broadcast (FFFF.FFFF.FFFF) as the destination address
• Since the ARP request is a broadcast, it reaches all the nodes in the Subnet A, including the router's e0 interface, but does not reach Host X. The broadcast will not reach Host X because routers, by default, do not forward broadcasts
• Since the router knows that the target address is on another subnet and can reach Host X, it will reply with its own MAC address to Host A
• The proxy ARP reply packet is encapsulated in an Ethernet frame with router's MAC address as the source address and Host A's MAC address as the destination address. The ARP replies are always unicast to the original requester
• On receiving this ARP reply, Host A updates its ARP table
• From now on Host A will forward all the packets that it wants to reach Host X to the Routers MAC address
• Since the router knows how to reach Host X, the router forwards the packet to Host X. The ARP cache on the hosts in Subnet A is populated with the MAC address of the router for all the hosts on Subnet B
• Hence, all packets destined to Subnet B are sent to the router.
• The router forwards those packets to the hosts in Subnet B.