放心 fàngxīn — to set one’s mind at rest, to stop worrying

fàngxīnfang4xin1

to set one’s mind at rest, to stop worrying

HSK 3· HSK 1–6 (classic)Level 2· 2021 three-band, nine-level proficiency standardverb

Meanings

to set one’s mind at rest, to stop worrying
Literally to put 放 the heart 心 down. It is the answer to 担心: one person worries, the other says 你放心. As a two-part verb it takes no object — the person you feel easy about is introduced with 对.
verb

放
fàng (fourth tone, falling)
to put, to place, to lay down; to let go, to release, to set free; to let out, to give a holiday
8 strokes⿰方攵Radical 攴
心
xīn (first tone, high and level)
heart; mind, feelings, intention; the centre of something (中心)
4 strokesRadical 心

你放心，我一定会来。你放心，我一定會來。Nǐ (third tone, dipping) fàngxīn, (fourth tone, falling) wǒ (third tone, dipping) yídìng (second tone, rising) huì (fourth tone, falling) lái. (second tone, rising)···
Don’t worry — I will definitely come.
妈妈不放心我一个人去。媽媽不放心我一個人去。Māma (first tone, high and level) bú (second tone, rising) fàngxīn (fourth tone, falling) wǒ (third tone, dipping) yí (second tone, rising) ge (neutral tone) rén (second tone, rising) qù. (fourth tone, falling)···
Mum is uneasy about my going on my own.

Not quite我放心你。
Correct我对你很放心。
放心 already contains its object — the 心 you are putting down — so a second one cannot follow. Who you feel easy about is marked with 对 before the verb.