Final answer:
Traceroute is the appropriate tool on Linux to measure the final hop count for a packet in a mesh network as it records the route through the Internet and shows all intermediate routers.
Step-by-step explanation:
The proper tool to measure the final hop count for a packet in a mesh network using ICMP packet requests on Linux is traceroute. This network diagnostic tool records the route through the Internet from the host system to a target destination and lists all the intermediate routers that are traversed, providing the hop count. By default, traceroute sends out UDP packets, but it can also be configured to send ICMP echoes using the -I option on Linux. However, you should not confuse traceroute with tools like ping, which sends ICMP echo requests to just the destination to check the connectivity and measure round-trip time, or ARP, which resolves the network layer address into the link layer address, or dig, which queries DNS servers to get domain name information. None of these other tools would provide the hop count information you're seeking.