Which of the following terms describes the principle that groups of people with shared characteristics, such as language and culture, should be allowed to control their own governments?
a. communism
b. mandate system
c. self-determination
d. russification

C. Self-determination

The principle of self-determination was one of the key features of Woodrow Wilson's 14 Points, which he outlined as ways to bring The Great War (World War I) to an end and work toward a peaceful world. The intention to give people's the right to determine and control their own governments was embedded in sevedral of Wilson's points, such as:

Point #9. Readjustment of the borders of Italy "along clearly recognizable lines of nationality."

Point #10. Austria-Hungary retain a place among the nations, but the peoples of Austria-Hungary should be granted the accorded for independence if they so choose.

Point #12. Turkey shall remain as its own country, but other nationalities under the Ottoman Empire "should be assured an undoubted security of life" and "opportunity of autonomous development."

The "opportunity of autonomous development" (self-determination) wasn't exactly implemented everywhere as Wilson hoped. The "Mandate system" mentioned in the question options was a way in which European powers were entrusted to govern regions that were not deemed ready yet to govern themselves -- such as in former imperial holdings of Germany and the Ottoman Empire.

b) they want the land taken away from the wealthy landowners and given to peasants.