Final answer:
New Mexico and Arizona were the two states admitted to the union during the Taft administration.
Step-by-step explanation:
The two states admitted to the union during the Taft administration were New Mexico and Arizona. New Mexico was admitted on January 6, 1912, and Arizona on February 14, 1912. These state admissions occurred during William Howard Taft's presidency, which spanned from 1909 to 1913. Taft, who succeeded Theodore Roosevelt, was the 27th President of the United States and saw the country grow with the addition of these two states.