The correct matches are:
North - Gobi; Desert;
The northern part of China is dominated by desert. It is the Gobi desert that occupies large portion of this part of the country. The Gobi deserts the northernmost desert in the world. It is classified as cold desert as it has both hot summers , and very cold winters.
East - Coastal plains; Fertile river valleys;
The eastern part of China is where the Chinese civilization appeared, and where it developed and became what it is nowadays. This is a region dominated by coastal plains and very fertile river valleys. It is where the country has developed the most, the biggest cities have rose, and most of the population lives.
West - Mountains; Himalayas;
The western part of China is largely dominated by mountain ranges, the Tibetan Plateau, and the highest mountain range in the world, the Himalayas. It is a part of the country that doesn't offer good conditions for living or development, thus the population density is very low.