Final answer:
The best management for a 4cm by 4cm rhomboid facial defect after basal cell carcinoma excision in an elderly patient would be a local rotational flap due to its superior cosmetic outcomes on the face.
Step-by-step explanation:
The best option for managing a 4cm by 4cm rhomboid defect on the cheek of a 68-year-old lady after excision of a basal cell carcinoma is likely to be c. local rotational flap. This method allows for the movement of tissue from an adjacent area to cover the defect, ensuring a good cosmetic result and color match, which is crucial on the face. Options like a split thickness skin graft might not provide the best aesthetic outcome, while a pedicled myocutaneous flap is usually reserved for larger defects or when local tissue is not available. Both delayed primary closure and direct primary closure are typically not feasible for a defect of this size located on the face.