Friedrich Engels developed an early theory of family life making the claim that men gained control of women's sexuality as a means to protect their own wealth. This claim is the foundation for which type of theoretical analysis

social-conflict analysis

Explanation:

In sociology, Karl Marx was denoted as the father of the "social conflict theory".

Social conflict theory is described as a phenomenon that sees or look for individuals social life as a mode of competition and is focused on the distribution of power, inequality, and resources. However, various 'conflict theorists' is focused on viewing a particular society as an arena or place that consists of inequality and therefore generates or develops social change and social conflict.

The correct answer for the given question is social-conflict analysis.