How to take 4 coordinates manually in android just like on the website ?

eh, what? Sorry, please describe that with much more words. Also please explain what you already know about OSM and what specifically your problem is.

So I want to create a patrolling app of a neighbourhood.I know how do parse osm data and how to download it...that's on the server side. What i don't know is how to let the client(android side) to choose the coordinates of the area he want's to patroll...si i need something like on the osm site where i can manually export some rectangle on the map. I want the client to be able to select that rectangle. And after that how to draw on it the path I calculate on the server side. Thanks for much for the response.

so you want to know a Android map framework (for your Android app) which offers you some input like if you click "Manually select a different area" at https://www.openstreetmap.org/export and you want to display some poly-line on a map like the blue line in http://umap.openstreetmap.fr/de/map/unbenannte-karte_76136#10/52.4690/13.4122 , right?

Yes.And the poly-line could be with arrows :D but i will deal with that when i get there. Can you help me?

no, sorry, I am not really an Android dev, but I hope I could help to clarify your question. The only advise I could give is to look at the frameworks which are used by the open source Android apps. Just wait some days, others may help here!