The problem is as follows: The diagram shows a sequence of letters displaying the word "NOSUBASABUSON". How many ways can this word be read?.
The alternatives given are:
$\begin{array}{ll} 1.&3200\\ 2.&2480\\ 3.&3000\\ 4.&1600\\ \end{array}$
How exactly can I find those ways?. What I've attempted to do is to count individually from the left to the right and adding in tandem all of them.
This can be seen in the sketch from below:
But the part where I'm confused is what would it be the total. Adding the last column results in $400+400+800=1600$ ways.
But this can be read in two ways from left to right and from right to left. Which accounts for two ways but upon looking in the S where it is labeled by $40$ I could spot that you can read the word form that place and returning back to the right. But I don't know how to account for that way.
Thus I am not sure if it would be $3200$ or $4800$?. Can someone help me here?. Can an answer please include some drawing so I could see if my approach was right?.