Twenty-sixth Amendment to the United States Constitution
First of all, the states did not want to deal with the cost and difficulty of having to keep two different voting registers, so they supported the idea of a Constitutional amendment.  Also, when they changed the Voting Rights Act, Congress had made a law about state and local elections without the states having any say.  However, for an amendment to be added to the Constitution, two-thirds of both Houses of Congress, and then three-fourths of the state legislatures, have to agree on it.  (These rules are set out in Article Five of the Constitution.)  An amendment would be something that both Congress and the states agreed on.  Congress would not be over-using its power and breaking the Constitution by making laws for the states.