点头; 点了点头
点头 (diǎntóu) means "to nod" or "to nod one's head," typically indicating agreement, acknowledgment, or greeting. It is a verb-object compound combining 点 (to dot/to dip) and 头 (head). Because the object 头 is built in, the verb and object can be separated, as in 点了点头 (nodded).
老师问他听懂了没有,他点头说懂了。
Lǎoshī wèn tā tīngdǒng le méiyǒu, tā diǎntóu shuō dǒng le.
The teacher asked him if he understood, and he nodded and said he did.
她微笑着向我点头打了个招呼。
Tā wēixiào zhe xiàng wǒ diǎntóu dǎ le gè zhāohu.
She smiled and nodded to greet me.
经理听完汇报后满意地点了点头。
Jīnglǐ tīng wán huìbào hòu mǎnyì de diǎn le diǎntóu.
The manager nodded with satisfaction after hearing the report.