Question

During their early histories, ______ sometimes influenced Chinese government, while ______ sometimes influenced Indian government. Daoism; Confucianism Shinto; Hinduism Shinto; Buddhism Confucianism; Hinduism

Answer 1

Confucianism, Buddhism 
would be my best guess... but out of the answers you listed they probably want Daoism and Confucianism. 

Since Shinto is Japanese and Hinduism is Indian... those two are completely out of the question. 
_____ 
Daoism isn't really a government influence... it embraces the philosophy of yin and yang. Good and Bad, without one the other cannot exist. Natural influences of a good and bad government doesn't really make a good governing philosophy. Confucianism was really based on good and virtuous, people live life in harmony and proprietary. He's missing the rules and laws of the Legalist system of government. Where it assumes all people are bad and without laws and rules everything would be in chaos. The First Emperor established the Legalist system in China, he was said to have buried alive hundreds of Confucian scholars and burned Confucian books... His reign was short lived, only 14 years. The next dynasty... the Han, governed with a combination of Legalist and Confucian type of government, lasted 426 years. This pretty much continued till the Tang dynasty when Buddhism a larger influence in society.

Answer 2

Daoism for the first blank; Hinduism for the second blank. Hinduism is a way of life and it influenced the people and government. Daoism too. :)