In the array below, in how many different ways can we start with the letter A and move from letter to letter (horizontally, vertically, or diagonally), to spell the word "ARCH"?
I'm gonna take a guess here and say that your diagram meant to look like this:
This can be done with a simple counting principle:
( I actually don't know how to do this that well so I'm taking a wild guess)
From the first to the second we have 3 possible ways.
From the second to the third we also have 3 possible ways.
From the third to the fourth we again have 3 possible ways.
SO, my wild guess says the answer is 27 (but it was a wild guess so check it.