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Without allowing backtracking along edges

$60$

Since

"L" only appears at the four corners, and staring at any corner there are fifteen paths to form the word. $15\times 4=60$

The paths

From a corner there is $1$ way to reach the opposite corner, $5$ ways to reach each of the $2$ adjacent corners, and $4$ ways to come back without back tracking along edges ($2$ directions around the $2$ small triangles). $1+2\times 5+4=15$

Without allowing backtracking along edges

$60$

Since

"L" only appears at the four corners, and staring at any corner there are fifteen paths to form the word. $15\times 4=60$

The paths

From a corner there is $1$ way to reach the opposite corner, $5$ ways to reach each of the $2$ adjacent corners, and $4$ ways to come back without back tracking along edges ($2$ directions around the $2$ small triangles). $1+2\times 5+4=15$

Without allowing backtracking along edges

$60$

Since

"L" only appears at the four corners, and staring at any corner there are fifteen paths to form the word. $15\times 4=60$

The paths

From a corner there is $1$ way to reach the opposite corner, $4$ ways to reach each of the $2$ adjacent corners, and $4$ ways to come back without back tracking along edges ($2$ directions around the $2$ small triangles). $1+2\times 4+4=15$

Without allowing backtracking along edges

$60$

Since

"L" only appears at the four corners, and staring at any corner there are fifteen paths to form the word. $15\times 4=60$

The paths

From a corner there is $1$ way to reach the opposite corner, $5$ ways to reach each of the $2$ adjacent corners, and $4$ ways to come back without back tracking along edges ($2$ directions around the $2$ small triangles). $1+2\times 5+4=15$

$60$

Since

"L" only appears at the four corners, and staring at any corner there are fifteen paths to form the word. $15\times 4=60$

Without allowing backtracking along edges

$60$

Since

"L" only appears at the four corners, and staring at any corner there are fifteen paths to form the word. $15\times 4=60$

The paths

From a corner there is $1$ way to reach the opposite corner, $4$ ways to reach each of the $2$ adjacent corners, and $4$ ways to come back without back tracking along edges ($2$ directions around the $2$ small triangles). $1+2\times 4+4=15$