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Answer

Correct Option is 18

There are two ways of doing it. 

Technique 1: The Long one and obvious You keep counting the number of routes starting from S to U to V to T. 

Technique 2: Short cut Multiply the number of nodes from S, U and V leading towards T. It is 3 X 2 X 3 = 18. Reason: Each path that you will start on (lets say from S) will have to go through all the paths Number of ways you can reach U from S is 3. The number of ways you can reach V from U is 2. So the number of ways you can reach from S to V will logically be 3 X 2 = 6. Similarily logically extend it to T, it becomes 6X3 =18. 

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