[promise] {sb} the (moon|earth|world)

to make promises that are impossible to be fulfilled or be kept

The phrase "promise someone the moon" is an idiomatic expression that denotes making impractical promises or commitments to someone. The exact origin is not precisely documented, but it is rooted in the idea of offering something extremely grand or valuable, such as the moon, earth, or the entire world, as a pledge.

The politician promised the moon during the campaign, but many people were disappointed by the lack of progress after the election.
When he proposed to her, he promised her the world, a life of luxury, and endless happiness.
The CEO vowed to give his employees the earth when they reached their target, but they soon realized it was just talk.
She told her kids that if they cleaned their rooms, she would give them the moon, meaning a special treat or reward.
The coach assured the team that if they won the championship, he would give each player the moon, meaning an extraordinary reward, which motivated them to win.