AMC 8 2017 Problem 15

In the arrangement of letters and numerals below, by how many different paths can one spell AMC8? Beginning at the A in the middle, a path only allows moves from one letter to an adjacent (above, below, left, or right, but not diagonal) letter. One example of such a path is traced in the picture.

$\textbf{(A) }8 \textbf{(B) }9 \textbf{(C) }12 \textbf{(D) }24 \textbf{(E) }36$