Answer :

Starting from any one of the N's, there are 17 different readings of NAH, or 68 (4 times 17) for the 4 N's.
Therefore there are also 68 ways of spelling HAN.
If we were allowed to use the same N twice in a spelling, the answer would be 68 times 68, or 4,624 ways.
But the conditions were, "always passing from one letter to another."
Therefore, for every one of the 17 ways of spelling HAN with a particular N, there would be 51 ways (3 times 17) of completing the NAH, or 867 (17 times 51) ways for the complete word.
Hence, as there are four N's to use in HAN, the correct solution of the puzzle is 3,468 (4 times 867) different ways.

Math Genius