Through what modern day countries do the yellow and yangtze rivers flow

Both of river are passing through China.

The Yellow River is the next longest river in Asia, following the Yangtze River, and the sixth longest river system in the world at the predicted range of 5,464 km.  Arising in the Bayan Har Mountains in Qinghai region of Western China, it runs into nine provinces, and it leaves into the Bohai Sea near the city of Dongying in Shandong province.

The Yangtze River, 6,380 km long, is the longest river in Asia and the third longest in the world. The river is the longest in the world to pass completely within one country. It diminishes one-fifth of the state territory of the People's Republic of China (PRC) and its river sink is home to approximately one-third of the country's community. The Yangtze is the sixth-largest river by outflow capacity in the world.