How was the new hampshire colony successful.

 C) US Supreme Court

Explanation:  Generally speaking, a state supreme court is the court of last resort in any state, and the US Supreme Court is the court of last resort for federal cases.  US Legal offers this definition of "court of last resort" -

A court of last resort is the highest judicial body within a jurisdiction's court system. It is a court with the highest appellate authority, meaning that its rulings are not subject to further review by another court. A court of last resort is often, but not always, referred to as a supreme court.

It is possible to appeal a state supreme court decision to the US Supreme Court if there is a question of law under the US Constitution.  A "question of law" means there is a question regarding interpretation of a law.  It is different from a "question of fact," which pertains to the facts of a case.  So in your example, Yethreb's appeal would need to cite some matter of interpretation of law under the Constitution in order to appeal his case from the Ohio Supreme Court to the US Supreme Court.