give someone a hand—
1. help smb. with a task, etc.:
- Give me a hand with this case, will you?
2. applaud a person:
- Come on, give them a hand. They did very well.
Note: The expression does not correlate in meaning with the phrase give someone a free hand—give smb. freedom of action in affairs:
- He accepted the job after the prime minister agreed to give him a free hand in key economic issues.
give someone one’s hand—
1. agree formally to smth.:
- Yes, I agree to your marrying my daughter, and I give you my hand upon it.
2. (of a woman) agree to marry a man:
- Bruno and Evandra have loved each other for six years, but she refuses to give him her hand.