Which amendment process requires two-thirds of both houses and three-fourths of the states?

The amendment process outlined in the Constitution indeed requires a two-thirds majority in both houses of Congress and the ratification by three-fourths of the states. This rigorous process ensures that any amendments to the Constitution have widespread support among both federal and state legislators, reflecting a consensus that is necessary for such significant changes in the foundational legal document of the United States.

In comparison to the other options, the Articles of Confederation did not provide a clear and simple process for amendment, requiring unanimous consent from all states, which proved to be impractical. The Bill of Rights, while essential to the Constitution, is a collection of the first ten amendments rather than a standalone amendment process. Finally, the New Jersey Plan was a proposal during the Constitutional Convention focused on the structure of government, not on the amendment process itself. Thus, the Constitution stands out for establishing the specific amendment framework requiring two-thirds and three-fourths approval.