Math Trivia : Single stroke drawing

This figure is drawn with a single stroke of the brush. 
How many ways of drawing are there in all?

12 ways

Starting to draw from A or B.

When starting to draw from A, there are three ways of drawing direction. 

At B there are two ways of direction.
Therefore, there are 2 × 3 × 2 = 12 ways in total.

Which figures can be drawn by single stroke ?

 ②and ④