On the -plane, the origin is labeled with an . The points , , , and are labeled with 's. The points , , , , , , , and are labeled with 's. The points , , , , , , , , , , , and are labeled with 's. If you are only allowed to move up, down, left, or right by one unit at each step, starting from the origin, how many distinct paths can be followed to spell the word MATH?
