how did asian and african nationalists modify these western-inspired ideas with local cultural and political traditions to create unique movements of their own?

Asian and African nationalists based their ideologies on Western style democracy as they called for self-rule whereby the majority people could have a system of governance whereby they elected their leaders. They proposed the founding of their nations on the basis of the need to protect certain fundamental freedoms of their people.

Possible Answers:

People in India adapted their Western education to fit the multi-religious society of India.

The independence movement in India included a move to eradicate the caste system.

The Marxist ideology was adopted in China to fit peasants living in rural areas.