Pair 1 is incorrect. The Mekong River originates in the Tibetan Plateau and flows through China, Myanmar, Laos, Thailand, Cambodia, and Vietnam before emptying into the South China Sea, not the Andaman Sea.

Pair 2 is incorrect. The Thames River flows entirely within England and empties into the North Sea, not the Irish Sea.

Pair 3 is correct. The Volga River is the longest river in Europe. It originates in Russia and flows into the Caspian Sea.

Pair 4 is correct. The Zambezi River originates in Zambia and flows through Angola, Namibia, Botswana, Zimbabwe, and Mozambique before emptying into the Indian Ocean.

So, the correct pairs are 3 and 4. Hence, option C is the correct answer.