I got a hexagonal grid (cube coords)

[![enter image description here](https://i.stack.imgur.com/XbdCy.png)](https://i.stack.imgur.com/XbdCy.png)

In hex (0,0,0) there is a soldier and in another (distance == 4 hexes) a target:

[![enter image description here](https://i.stack.imgur.com/pO61y.png)](https://i.stack.imgur.com/pO61y.png)

i need to find all possible pathes from soldier hex to a target :

1)Length of path should be no more then 6 hexes

2)Not including those which returning to already visited tiles

3)Including those that are longer than the shortest possible path .

Though i need to solve it on javascript, but even pseudocode or just some thougths would be helpful

Thank you !