Question 1134175
<br>
To get from A to B, you have to move, in some order, 4 units forward ("F"), 4 units left (L"), and 4 units down ("D").<br>
The number of different paths from A to B is the number of different orders in which you can make those moves.  That is, the number of different paths is the number of different ways of ordering the moves FFFFLLLLDDDD.<br>
By a well-known counting principle, the number of different ways to arrange those moves is<br>
{{{12!/((4!)(4!)(4!)) = 34650}}}<br>
ANSWER: 34,650 different paths.  (don't try to count them all......)