Final answer:
In VoIP systems, the QoS mechanism responsible for compressing Layer 3 and Layer 4 headers is Compression. This process is crucial for bandwidth efficiency and maintaining call quality.
Step-by-step explanation:
The Quality of Service (QoS) mechanism that can compress the Layer 3 and Layer 4 headers of a voice over IP packet is c) Compression. Compression is used in networking to reduce the size of packets to save bandwidth and improve transmission speeds. In VoIP, header compression is particularly useful because it reduces the overhead, allowing for more efficient use of network resources, which is essential for maintaining good call quality. While other QoS mechanisms like traffic shaping, fragmentation, and classification manage the bandwidth and priority of traffic, they do not perform compression of headers.