Breyer denied cert (not taking the case) initially becaue he couldn't get 5 votes. A little later, after he persuaded Kennedy, he told the Boumediene attorney to applyl for cert again.
It took four votes for SC to take the case, and five vote (in most cases) to rule. Breyer and three liberals would have voted to take the case, but Breyer decided to vote against taking the case intially for the above reason, therefore at first the case only got 3 votes in the court thus failed.
But From wikipedia
In February 2007, a three-judge panel of the Appeals Court for the D.C. Circuit considered Lakhdar Boumediene's habeas corpus submission, and in a split decision, upheld the Congress's authority to quash the outstanding habeas corpus submissions.[7] In April 2007, the Court declined to review the Circuit Court's decision.
Within a few months, it reversed this decision; on June 29, 2007, it granted a writ of certiorari to Boumediene and his co-defendants.[8][9]