The correct answer is option 4, Central Asia. The Taklamakan Desert is one of the largest sandy deserts in the world and is located in Central Asia. It is bounded by the Kunlun Mountains to the south, the Pamir Mountains to the west, and the Gobi Desert to the east. The desert is located within the Xinjiang Uyghur Autonomous Region of China.

Option 1, Western Asia, is not correct for the location of the Taklamakan Desert. Western Asia refers to the region that includes countries like Turkey, Iraq, Iran, and Syria, but the Taklamakan Desert is not located in any of these countries.

Option 2, the Southern fringe of Sahara in Africa, is also incorrect. The Sahara Desert is located in Northern Africa and is not connected to the Taklamakan Desert.

Option 3, South America, is not correct either. The Taklamakan Desert is not located in South America, but rather in Central Asia, as mentioned earlier.

Therefore, the correct answer is option 4, Central Asia.