Step 1: Understand frog respiration.
Frogs are amphibians and can use skin, buccal cavity, and lungs depending on where they are.
Step 2: Focus on the water condition.
The question asks how a frog breathes while it is in water.
Step 3: Identify the surface used.
Underwater the frog uses its thin, moist, vascular skin for gas exchange, a process called cutaneous respiration. So the answer is skin.
Step 4: Explain the exchange.
Dissolved oxygen diffuses through the skin into the blood while carbon dioxide passes out into the water.
Step 5: Reject lungs and buccal cavity.
Lungs and the buccal lining are used mainly on land, and the lungs stay inactive when the frog is submerged.
Step 6: Reject trachea and conclude.
Frogs have no breathing trachea like insects, so the correct underwater respiratory organ is the skin.
\[ \boxed{\text{skin}} \]