Final answer:
Rufus King carried three states in the 1816 election, but the options provided do not match the information given.
Step-by-step explanation:
In the 1816 election, Rufus King carried three states.
According to the information provided, Lincoln carried all free states except for New Jersey, while Breckinridge carried 11 of the 15 slave states. Since the question specifically asks about Rufus King, who was a candidate in the 1816 election, we can conclude that he carried three states.
However, it's important to note that the options given in the question (5, 8, 12, 17) do not match the information provided. Therefore, the correct answer cannot be determined based on the given options.