What must occur for state legislatures to propose an amendment to constitution
One-half of state legislatures must vote to propose the amendment
Two-thirds of congress must vote to propose the amendment
Three-fourths of state legislatures must vote to propose the amendment ***
One-fourth of congress must vote to propose the amendment
To propose an amendment to the constitution, three-fourths of state legislatures must vote in favor of the amendment.
To get the answer to this question, you can refer to the process outlined in Article V of the United States Constitution. According to this article, there are two ways to propose amendments:
First, Congress can propose an amendment by a two-thirds majority vote in both the House of Representatives and the Senate. This method is often used and has been used for all existing amendments so far.
Alternatively, if two-thirds of state legislatures (which is currently 34 out of 50) pass resolutions calling for a constitutional convention, then such a convention can be held. Any proposed amendments that come out of this convention must then be ratified by three-fourths of state legislatures (which is currently 38 out of 50) in order to become part of the constitution.
In summary, while two-thirds of Congress can also propose amendments, the answer to your question is that three-fourths of state legislatures need to vote in favor of an amendment to propose it.
http://www.archives.gov/federal-register/constitution/
Read carefully.