在乎 zàihu to rest with

to rest with; to lie in; to be due to (a certain attribute); (often used in the negative) to care about

怎么记住“在乎”: 在 at + 乎 a call = to rest with.

汉字

在乎 (zàihu) means "to care about/mind," and is most natural in the negative or in questions: 不在乎 (bú zàihu, doesn't care), 你在乎吗? (Do you care?).
It answers "does this matter to me emotionally," not "do I know about it" - 我不在乎别人怎么想 (wǒ bú zàihu biérén zěnme xiǎng) - I don't care what others think.
Compare with 关心 (guānxīn), which is caring for someone out of concern/warmth (like a parent caring about a child's health) - 在乎 is about whether something affects or bothers you personally.
Also close to 介意 (jièyì, to mind/be bothered by something specific) - 在乎 is broader and more emotionally loaded, often about relationships (在乎一个人 = to really care about a person).