Final answer:
The most stable area for supporting a mandibular complete denture is the Buccal shelf due to its dense bone, resistance to resorption, and strategic positioning which counters occlusal forces efficiently.
Step-by-step explanation:
The most stable area for support of a mandibular complete denture is the Buccal shelf. The buccal shelf is an area of dense bone that is resistant to resorption and is located on the lateral aspect of the lower jaw, under the alveolar process of the mandible where the lower teeth are anchored. It provides excellent stability due to its position being at right angles to the occlusal plane, which allows it to efficiently counteract the forces of occlusion. This stability is further enhanced by its location overlying the superior aspect of the body of the mandible, which keeps it away from the dislodging forces of the tongue and soft tissues.
Other anatomical landmarks such as the retromylohyoid area, residual ridge, mylohyoid ridge, and genial tubercle may also provide denture support but are not as stable as the buccal shelf because of the varying degree of resiliency of the mucosa overlying these structures and the potential for bony resorption in these areas.