两liǎng全quán其qí美měi

Literal: both kept whole, the good of each
Figurative: A solution that reconciles two interests or two parties that seemed at odds, so that neither has to lose out; the best of both worlds.

Where does 两全其美 come from?

It does not come from a specific anecdote; its characters explain it. 两全 means "both things kept whole," with neither swallowing the other, and 其美 adds "with the good of each." The phrase already appears in Yuan-dynasty drama, in the anonymous play 《连环计》, which stages the scheme by which the minister Wang Yun turned Dong Zhuo and Lü Bu against each other. Today it is used in everyday life and at work to welcome an arrangement in which nobody has to give up what matters most to them.

Source (出处): 《连环计》

How is 两全其美 used? Two examples

周zhōu末mò上shàng午wǔ我wǒ陪péi你nǐ逛guàng街jiē，下xià午wǔ你nǐ陪péi我wǒ看kàn球qiú，不bù就jiù两liǎng全quán其qí美měi了le？
This weekend I'll go shopping with you in the morning and you'll watch the game with me in the afternoon. That way we both get what we want, right?
公gōng司sī允yǔn许xǔ每měi周zhōu在zài家jiā办bàn公gōng两liǎng天tiān，员yuán工gōng省shěng了le通tōng勤qín时shí间jiān，公gōng司sī省shěng了le房fáng租zū，两liǎng全quán其qí美měi。
The company lets staff work from home two days a week: employees save on commuting and the company saves on rent. Everyone comes out ahead.

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