For the first question about which method Mao did NOT use to maintain his power, the correct answer is:
D. Allowing democratic reforms demanded by protesters.
Mao Zedong did not allow democratic reforms; rather, he used authoritarian methods to suppress dissent.
For the second question regarding Mao's greatest achievement in China, the correct answer is:
A. Winning the civil war and establishing a communist state.
This was indeed Mao's most significant achievement, as it established the People’s Republic of China in 1949.