Donne-moi un coup de main, veux-tu?
DUN-mwah uh coo duh MAA, vuh-TEW?
Give me a hand, will you?
Help me, in other words. (The veux-tu at the end is a way to make your request more polite.)
On the other hand (par contre, paar KAW-truh), Donne-moi la main means Give me your hand (so you can propose marriage, tell someone’s fortune, or give away your used chewing gum).
And Ils se sont donnés la main means They shook hands: they gave each other their hand. A French handshake is not really a shake at all: it’s a firm grasp and a single pump up and down.
What about Ils se sont secoués les mains? They shook their hands. That’s what you do when the paper towels are gone, or to get rid of that sticky chewing gum!