First, notice that the graph has exactly 6 vertices of odd degree.

wpe7.jpg (19848 bytes).

Now add duplicate edges to reduce the total number of odd vertices to 2.

wpe8.jpg (19602 bytes)

 

So, this graph was Semi-Eulerized by adding 2 duplicate edges.

(Any Euler Path would begin at one of the remaining odd vertices and end at the other.)

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