## Core Concept
The question involves understanding the anatomy of the wrist and hand, specifically the arrangement of tendons and synovial sheaths. The extensor digitorum tendons are surrounded by a synovial sheath as they pass through the third compartment of the wrist.

## Why the Correct Answer is Right
The extensor digitorum tendons, which control finger extension, pass through a synovial sheath in the third dorsal compartment of the wrist. The extensor indicis tendon, which also facilitates finger extension, shares the same synovial sheath as the extensor digitorum tendons. This anatomical arrangement allows for smooth movement and reduced friction between these tendons.

## Why Each Wrong Option is Incorrect
* **Option A:** The extensor pollicis longus tendon is located in the third dorsal compartment but is surrounded by its own synovial sheath. It primarily facilitates thumb extension.
* **Option B:** The extensor pollicis brevis tendon, along with the abductor pollicis longus, is in the first dorsal compartment and has its own synovial sheath. It aids in thumb extension and abduction.
* **Option D:** The flexor digitorum profundus and superficialis tendons are surrounded by a synovial sheath but are located in the palm and fingers, within the flexor tendon sheath, not the extensor sheath.

## Clinical Pearl / High-Yield Fact
A key point to remember is that the extensor tendons at the wrist are organized into six dorsal compartments. The third compartment contains the extensor digitorum and extensor indicis tendons, which share a synovial sheath. This arrangement is crucial for understanding tendon injuries and tenosynovitis.

## Correct Answer Line
**Correct Answer: B. extensor indicis.**