A more thorough explanation:

The adequate-state-grounds doctrine is a principle created by judges that stops the U.S. Supreme Court from reviewing a decision made by a state court if the decision was based on state law and a decision on a federal issue would not change the outcome.

For example, if a state court decides a case based on a state law that is different from a federal law, and the outcome would be the same regardless of which law was used, the U.S. Supreme Court would not review the case. This is because the state court's decision was based on adequate state grounds, and there is no need for the federal court to intervene.

Another example is if a state court decides a case based on a state constitutional issue, and the outcome would be the same regardless of whether a federal constitutional issue was considered. In this case, the U.S. Supreme Court would not review the case because the state court's decision was based on adequate state grounds.

These examples illustrate how the adequate-state-grounds doctrine works in practice. It allows state courts to make decisions based on their own laws and constitutions without interference from the federal court system, as long as the decision is not affected by federal law or constitutional issues.