Step 1: Anchor the answer on wrist surface anatomy. The radial side of the wrist has six dorsal extensor compartments, and De Quervain disease is the classic disorder of the very first one.
Step 2: A quick rule for compartment one is $APL + EPB$ - two tendons only. Both run together over the radial styloid, and thickening of their shared sheath causes the localised pain of De Quervain.
Step 3: Test each choice against this rule. Abduction of the thumb needs the abductor pollicis longus, so any option naming the adductor is anatomically false. The second tendon must be the extensor pollicis brevis, so any option naming a flexor is also false.
Step 4: Only option a pairs the abductor pollicis longus with the extensor pollicis brevis, both of which are extrinsic thumb tendons that genuinely traverse compartment one. Clinically, Finkelstein test reproduces the symptoms by stretching exactly these two tendons.
\[\boxed{\text{Abductor pollicis longus and extensor pollicis brevis}}\]