This is the Supremacy Clause that AG Garland was talking about in his annoucement.
Constitution of the United States of America - Article VI
All debts contracted and engagements entered into, before the adoption of this Constitution, shall be as valid against the United States under this Constitution, as under the Confederation.
This Constitution, and the laws of the United States which shall be made in pursuance thereof; and all treaties made, or which shall be made, under the authority of the United States, shall be the supreme law of the land; and the judges in every state shall be bound thereby, anything in the Constitution or laws of any State to the contrary notwithstanding.
The Senators and Representatives before mentioned, and the members of the several state legislatures, and all executive and judicial officers, both of the United States and of the several states, shall be bound by oath or affirmation, to support this Constitution; but no religious test shall ever be required as a qualification to any office or public trust under the United States.
This is essentially saying that no state may have State Constitutions or State Laws that contradict the US Constitution or Federal Laws. It also prohibits any state from interfering with the Federal Government's exercise of its Constitutional powers, and from assuming any functions that are exclusively entrusted to the Federal government.
It does not allow the Federal government to review or veto state laws before they take effect. I'm guessing this is the reason why the Garland and the DoJ have waited until now to bring the court action against Texas.