The difference between (mir die) and (meine)?
What is the difference between those two sentences ? -(Ich wasche mir die Hände.) and -(Ich wasche meine Hände.) They mean the same which is (I wash my hands) , So is there some rule when to use "mir die" and when to use "meine". Or they mean exactly the same and I can use both of them whenever I want to indicate the possession of my own hands. :D
As a native speaker i may confirm you there is no difference in meanings. They exactly mean the same, though, I feel "ich wasche meine Hände" is a little bit more common, but also "ich wasche mir die Hände" is absolutely a normal way of saying it, so that nobody would look irritated when you use it. :)
So in both ways everybody will understand you are washing your own hands and not any "artificial" hands or any other person's ones. ;)
Here's a native speaker who definitely seems to prefer the "mir" version: https://yourdailygerman.com/german-reflexive-verbs (long article, so easiest to search for "die Hände"). Ah well, native speakers (of any language) can of course disagree.
BTW, when you say "irritated", do you mean "confused"? I don't think German irritieren can always be translated as English irritate. When speaking about a person's reaction, "irritated" means "slightly annoyed".
I think I've read a comment somewhere (possibly on Duolingo?), which said if you had, say, a collection of artificial hands that you were washing, then "Ich wasche meine Hände" is what you would say. In other words, that sentence makes it sound like the hands in question are not part of your body. I hope I'm remembering that correctly!