Explanation:

- Assimilation: This is when a person or group completely adopts the cultural traits of another group, often losing their original culture in the process.

- Diffusion: This means the spread of cultural elements from one society to another through direct or indirect contact.

- Integration: This involves combining parts of different cultures while maintaining distinct cultural identities.

- Acculturation: This is the process through which individuals or groups adopt certain cultural traits of another group, but still retain some original cultural features.

The correct answer is Option:4 - Acculturation.

This happens when American Indians adopt some elements of mainstream American culture, but keep parts of their own traditions.