The correct option is A 2
We can find the routes that satisfy the given conditions by trial and error. But this can be time-consuming. Therefore, we can analyze the problem in the following way.
The figure is formed by two non-overlapping triangles, bed and bac. Three routes can be traced on each triangle without tracing any route twice. So, we try to find a route that helps us trace these two triangles independently.
The route dc connects the two triangles. So, if we choose 'd' as our starting point, we can trace triangle deb and come back to 'd', then travel to 'c' and trace triangle cab and come back to 'c'.
This can work even if we take 'c' as our starting point. This does not work with any other point.
Thus, there are only 2 islands, 'c' and 'd', which can be the starting points.