In this drawing there are 5 nodes total, and 4 of them are odd. Therefore, this puzzle is impossible. Remember: You can only solve a puzzle if it has TWO ODD NODES or NO ODD NODES. 

In this drawing there are 2 odd nodes, which means that there is a solution. In the case of 2 odd nodes, you must always start on one odd node and stop on the other. 

In this drawing there are no odd nodes, so this puzzle also has a solution. When there are no odd nodes, you will always stop at the same point you started on! 
...You may wonder and ask, "What if there is only ONE ODD NODE?" The answer is that it is IMPOSSIBLE to draw a figure with only a single odd node, even by cheating!