graph-theory task 
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Graph-theory exercise 

The picture below shows a graph connecting the cities А, Б, В, Г, Д, Е, Ж, И, К.

On each path you can only move only in direction of the arrow. How many different ways are there from city A to city K?
I understood that this exercise is from graph theory. Please tell me how I can solve exercises like this.
P.S. Sorry for my poor English. It isn't my native language. I would be very grateful if you would mention errors in my English.

Assume that the graph is acyclic.
Let $P(v)$ be the predecessors of $v$ (i.e. $P(v) = \{u : (u, v) \in V\}$).
Let $n_u(v)$ be the number of ways of reaching $v$ from $u$, where we define $n_u(u) = 1$.
Then, assuming no duplicate edges, $$n_u(v) = \sum_{w\in P(v)} n_u(w)$$
This is easily proven by induction over a topological sort of the vertices.
