It can be seen that the three points in the middle of the upper and lower sides of the figure and the one point in the middle of the left and right sides are eight points, which are connected by three lines respectively.

Anyone who has drawn a stroke knows that the points connected by odd lines are called odd points. As we can see, when passing through odd points, you must first pass a line to this point, and then leave this point along another line. The next time you pass this point along the third line, you must take a repeated line no matter where you start. Or, follow the line you have already walked to this point and leave from the third line, then you have to take a repeated line.

Therefore, if you want to walk all 22 edges in the graph, you must walk at least 8 repeated lines when passing through 8 odd points in the graph (because the topic has already said that you should start from the vertex).

So the shortest distance =22+8=30.

As for the specific ways, there are many kinds, and I only take one.

If you start from the upper left corner:

Down, down, right, up, left, right, right, down, left, right,

Right, up, left, right, right, down, left, up, right, up,

Left, down, left, up, right, left, left, down, up, left.

It's done.