I think HerrKlotz is asking if using "my" is correct when referring to my own body parts, that is "Meine Hand tut weh" or "Die Hand tut weh"? I have seen in another discussion that often the personal pronoun is not used for your own body part, contrary to English usage. For instance in Italian, my native language, I would never say "my hand hurts" but "the hand hurts" (mi fa male la mano). I think in French is similar.
On January 29, 1964, in Paris, the Beatles recorded German lyrics to their latest hit 1963 English release, as "Komm, gib mir deine Hand." Their diction is pretty good. I got to know it not from some German 45 single, but from the American album "Something New," which I played over and over and over. The German grammar makes way more sense to me now, though!
It's one of those words that can have several meanings.
If you see it written in the middle of a sentence, you can tell if it is lowercase ihre or uppercase Ihre:
Lowercase ihre means either "her" or "their". The grammar is the same for either, so you need to use context to decide which is more likely. Without context, either should be accepted by Duolingo.
Uppercase Ihre in the middle of a sentence means "your" in the polite/formal way - the situations when you would use Sie instead of du. As with Sie, you can use Ihre when talking to one person or to a group - there's no singular/plural difference like with du/ihr or dein/euer.
The pronunciation of all three meanings is the same, so if it was spoken it could be interpreted as any of those without context.
Reminds me of Llamas in Hats...
But "he held her hand" refers to the time which he was already holding it. "He took her hand" refers specifically to the action of first reaching out and holding it.
This distinction matters because maybe she was the one who reached for him - i.e. she took his hand. In that case, he was holding her hand, but he didn't take it.