It’s like the earlier problem. Work backwards from К: the only way to get there directly is from Е. Е can only be reached directly from В and Г. Г can be reached only from А, while В can be reached from Б or А, and Б can be reached only from А. If you backtrack from К to А, the first step must be to Е. After that you have two choices, В and Г. If you go to В, you have three choices: directly to А, Б to А, or Г to А. Thus, there are three routes back through В. If you go instead to Г, you have no further choices: you can only go to А. Thus, there are altogether four routes:
$\begin{align*} &\text{А}\rightarrow\text{Г}\rightarrow\text{Е}\rightarrow\text{К}\\ &\text{А}\rightarrow\text{В}\rightarrow\text{Е}\rightarrow\text{К}\\ &\text{А}\rightarrow\text{Б}\rightarrow\text{В}\rightarrow\text{Е}\rightarrow\text{К}\\ &\text{А}\rightarrow\text{Г}\rightarrow\text{В}\rightarrow\text{Е}\rightarrow\text{К} \end{align*}$
When you trace back, you see that only part of the graph actually matters:
Б / \ / \ А-----В \ / \ \ / \ Г-----Е-----К
(All arrows here are understood to point from left to right.)