Start bottom right or top left and draw the lines exceeding the square formed by the dots.
We seem to be programmed viewing the field created by the dots as limitation
and thus do not see the solution. A purpose of the riddle is to realize that
there are always solutions. Sometimes, we simply have to exceed limitations.
With this example given, we might be encouraged to reevaluate limiting patterns within our day-to-day lives and to raise the awareness.
When I first tried to figure out the riddle, I approached it logically, because that was the way I was trained in order to deal with things. I tried all possible line-dot-connections in every possible direction. From an analytical point of view, the solution had to be found by trying all possibilities.
But, by having been limited to the field, I failed finding the solution. I started doubting, I did not think there was a solution at all. Thus, I stopped trying for a while, although I was still hoping that I could somehow figure it out. I was not the only person trying to find a solution. The riddle was given to a group of people and some already knew the solution. It happened then, that one guy mentioned to go beyond the field. With that in mind, it was then rather easy to solve it.
What I learned through this exercise is, that our conventional analytical thinking is limited in some ways. Quite often, we tend to label things "impossible" too soon whereas the solution is easy and obvious. Sometimes it helps to go beyond conventional thinking.
Instead of thinking out fo the box get rid of boxes.