A bill that was signed by the Governor is challenged in court by citizens who claim that it harms the community. The Supreme Court listens to the arguments on both sides and makes a decision that the law is unconstitutional. In this case, are the justices interpreting the law or administering justice?
In this case, the Supreme Court would be interpreting the law.
From the facts presented, the Supreme Court is acting to interpret the law and the Governor's actions before determining that the Governor acted outside the boundaries of the law.