The answer is C: Credit Mobilier.
Explanation for each option:
a. Teapot Dome: This scandal occurred in the early 1920s, involving the secret leasing of federal oil reserves by the Secretary of the Interior, Albert B. Fall. It is not related to the events of 1872.
b. Red Shirt outbreak: The Red Shirts were a white supremacist paramilitary group active during the Reconstruction era, particularly in the late 19th century. However, there was no specific "Red Shirt outbreak" scandal in 1872.
c. Credit Mobilier: This was a major scandal in 1872 involving the Union Pacific Railroad and the Credit Mobilier of America construction company. High-ranking officials and members of Congress were implicated in receiving bribes and shares of stock in exchange for favorable legislation and contracts.
d. Libyan Embassy: This option is not relevant to the events of 1872. The Libyan Embassy incident likely refers to events much later in history, such as the 2012 Benghazi attack.
Therefore, the correct answer is C: Credit Mobilier.