This is the 2699th most frequent Polish word.
dali
"Dali" in Polish means "they gave."
In this sentence, 'dali' is the third person plural past tense of the verb 'dać', meaning 'to give'.
Dali mi piękny prezent na urodziny.
They gave me a beautiful gift for my birthday.
Here, 'dali' is part of the phrase 'dać radę', meaning 'to manage' or 'to succeed in doing' something.
Kiedyś dali radę rozwiązać ten problem sami.
Once they managed to solve this problem on their own.
In this context, 'dali' is part of the past form of 'dać znać', an expression meaning 'to inform' or 'to let someone know'.