The federal government tells the state of Wyoming that they must adopt new standards into their high school classrooms.
Wyoming's Department of Education says, "No, the states are in
charge of setting their education standards." Which amendment
would Wyoming cite? Why?

The 10th amendment states:

"The powers not delegated to the United States by the Constitution, nor prohibited by it to the States, are reserved to the States respectively, or to the people"

So basically the constitution lays out a list of powers that the federal government has (eg: the power to mint money). Any power not listed in the constitution is then given to the states, as long as that rule doesn't violate a power granted to the federal government.

Nowhere in the constitution does it mention anything about education standards, so it is up to the states to decide what schools should cover, and by what time schedule. And this power to the states is granted explicitly in the 10th amendment of the constitution.