Step 1: The marked structure is the first lumbrical muscle of the hand. The lumbricals are intrinsic muscles of the hand that flex the metacarpophalangeal joints and extend the interphalangeal joints.
Step 2: Most intrinsic hand muscles are supplied by the deep branch of the ulnar nerve. The two exceptions are the thenar muscles and the lateral two lumbricals.
Step 3: The lateral two lumbricals (to the index and middle fingers) and the thenar muscles are supplied by the median nerve. Recall the mnemonic MEAT-LOAF: Median nerve supplies the Lateral two lumbricals, Opponens pollicis, Abductor pollicis brevis and Flexor pollicis brevis.
Step 4: Because the first lumbrical is one of the lateral two, its nerve supply is the median nerve, making option (d) correct. The ulnar nerve (c) supplies only the medial two lumbricals, so it is wrong. The anterior and posterior interosseous nerves (a, b) are branches of the median and radial nerves respectively that do not innervate the lumbricals.