When an IS audit reveals that a firewall was unable to recognize a number of attack attempts, the auditor's BEST recommendation is to place an intrusion detection system (IDS) between the firewall…

Placing the IDS between the firewall and the web server might protect the web server, but it doesn't provide comprehensive protection for the entire internal organization's network against threats that bypass the firewall.

Placing the IDS between the firewall and the Demilitarized Zone (DMZ) is often a valid configuration for protecting DMZ resources, but the question implies a general protection for the "organization's network" against attacks that the firewall missed, which is better served by placing it deeper inside the perimeter.

Placing the IDS between the firewall and the Internet is redundant, as the firewall itself is typically the first line of defense at the perimeter, and an IDS would analyze traffic that the firewall is already inspecting or attempting to block.

Placing an Intrusion Detection System (IDS) between the firewall and the organization's internal network ensures that traffic after it has passed the firewall is further inspected for malicious patterns or anomalies. This provides an additional layer of security, catching threats that the firewall might have missed or that originate from within the perimeter, directly protecting internal assets.