Final answer:
Catherine the Great promoted Enlightenment ideas primarily through intellectual engagement and attempted reforms in governance, corresponding with Enlightenment thinkers and hosting salons, despite the authoritarian context of her rule.
Step-by-step explanation:
Catherine the Great, Empress of Russia, was known as an "enlightened despot" who, while maintaining an authoritarian rule, claimed to draw political power from the social contract, a key Enlightenment concept. She promoted the spread of Enlightenment ideas not through military conquests, strict censorship, religious orthodoxy, or advocacy of serfdom, but rather by engaging with the ideas themselves and applying a measure of them to Russian governance, despite Russia's overall conservative and autocratic political climate.
Catherine the Great supported Russian expansion and appreciated Enlightenment thoughts, particularly those concerning governance and law. She contributed to intellectual discourse by corresponding with prominent Enlightenment figures and attempting to enact reforms based on these principles, although her success was limited by various constraints, including the social structure of Russia and opposition from the conservative nobility.
Enlightenment ideas were predominantly exchanged in settings like salons, which were often hosted by elite women and served as a critical public sphere for the exchange of such progressive thoughts.