The BIG IP device is connected to the same network as a server. Which communication protocol will the BIG IP device use to discover the link layer address of the server?

Ping tests end-to-end IP reachability using ICMP echo messages and cannot resolve or discover link layer addresses.

ICMP is a network-layer protocol used for error reporting and diagnostics - it has no mechanism for resolving IP addresses to MAC addresses.

RARP (Reverse ARP) performs the opposite function - it discovers an IP address from a known MAC address - and is now a deprecated protocol.

ARP operates at the Layer 2/3 boundary by broadcasting a request asking which MAC address corresponds to a target IP on the local network. The target server replies with its MAC address, enabling the BIG-IP to forward frames directly to that server at the link layer - this is exactly the link layer address discovery described in the question.