10. Teacher Yangyang's city has 4 subway lines, each of which intersects with every other line at exactly one point, serving as the transfer station for those two lines. One day, Teacher Yangyang had a sudden idea to start from the subway station near her home (which is not a transfer station), make at least one transfer at each transfer station, and finally return home. How many transfers does Teacher Yangyang need to make to achieve her goal? $\qquad$ times.
【Answer】8
【Analysis】First, for 4 lines, each pair has a transfer station, so there are 6 transfer stations in total. Using connection points to represent subway lines and line segments to represent transfer stations, it can be represented as follows:
Then the problem becomes, starting from any point on the graph except for the 4 intersection points, how many line segments at least need to be passed to walk through all the line segments and return to the starting point. Using the idea of the one-stroke problem, it can be seen that the 4 points in the graph are all odd points. If you want to walk through all of them and the starting and ending points are not these 4 points, then these 4 points need to become even points, which means adding two more line segments in the graph. Therefore, a total of 8 line segments need to be walked to pass through each segment once, that is, at least 8 transfers are required for Teacher Yangyang to meet the requirements mentioned in the problem.