From the title and the key, it can be understood that this is a tangram puzzle. None of the numbers have a single, unique, solution, but they each always have the same piece in the same orientation in the location of the star. (In the cases of the 1 and the 2, some possible solutions have the star located in one of the two largest triangles. However, since those pieces are not associated with a letter according to the key, we can take that as an indication that we need to find a different solution. One possible solution for each puzzle is shown here:
Using the given key, each piece with a star can be paired with a letter. For example, the one has a star in a medium-sized triangle with the right angle in the upper right. Therefore, the first letter is K. Repeating this for all four puzzles gives KOAN, a paradoxical riddle from Zen Buddhism used to provide enlightenment, and the answer to this puzzle.