Problem Solving - Australian Maths

I entered a competition last year and got the results back 6 months later. I am going through the paper again now for preparation for this year's test and trying to solve the answers to the questions. I don't mean to brag, but I am an intelligent person when it comes to maths (I would have achieved first in my country for this if I wrote down the correct answer, I did the correct working and got the right answer but when i wrote it in I wrote it wrong :l) so this question really confuses me;

To match my hexagonally paved path, I built a Giant;s Causeway garden feature from 19 hexagonal stone columns, arranged in a hexagonal pattern with three different levels, as shown. In how many ways can I climb from S to F if I only step to an adjacent column, never step on any column twice and never step down a level?

Attached is the question (sorry about the bad quality but you can make out the shape). The answer to the question is 385 but I don;t know how to work that out and get the answer.

Help would be very much appreciated.

Many thanks, Abbie