if the president and vice president can't serve out their terms,the next person in line to govern is the??

This chart will give you the line of succession.

http://en.wikipedia.org/wiki/United_States_presidential_line_of_succession

If the president and vice president are unable to serve out their terms, the next person in line to govern is the Speaker of the House of Representatives. The Speaker of the House is the leader of the majority party in the House of Representatives and is second in line for presidential succession, after the vice president.

To find this information, you could refer to the United States Constitution, which establishes the order of succession in Article II, Section 1, Clause 6 and the Presidential Succession Act of 1947. These sources outline the line of succession and provide the Speaker of the House as the next in line after the vice president. Additionally, you can consult reputable government websites or civics textbooks that cover the topic of presidential succession in the United States.