Step 1: Recall the sustentaculum tali. It is a shelf-like bony projection on the medial side of the calcaneus that supports the talus. Its under-surface carries a groove.
Step 2: Identify the tendon in that groove. The flexor hallucis longus tendon runs in the groove on the under-surface (inferior surface) of the sustentaculum tali. This is why the structure helps pulley the tendon toward the great toe.
Step 3: Exclude the other tendons. Tibialis anterior crosses the front of the ankle and inserts on the medial cuneiform and first metatarsal, nowhere near the sustentaculum. Flexor digitorum longus passes medial to and just above the sustentaculum, not under it.
Step 4 (second part of the original question): The tendon that gains attachment on the sustentaculum tali is the tibialis posterior. Tibialis posterior inserts mainly on the navicular tuberosity but also sends slips to the sustentaculum tali and other tarsal and metatarsal bones, so its attachment is on the sustentaculum, whereas flexor hallucis longus merely grooves its under-surface.
Step 5: So the tendon passing below the sustentaculum tali is flexor hallucis longus, and the tendon attaching to it is tibialis posterior.
The answer is D. Flexor hallucis longus.