开口(kāi kǒu) - to open one's mouth, to start speaking, to bring oneself to ask in Mandarin

开口 (kāi kǒu) is to open your mouth, which in practice means to speak up after a silence. It marks the moment the speaking starts rather than the speaking itself, so it is the verb for someone who has been sitting quietly and finally says something.

The second, very common sense is asking a favour. 不好意思开口 is the exact feeling of knowing what you want but not being able to get the request out. Chinese leans on this a lot, and 张不开口 is the stronger version: your mouth simply will not open.

The English-speaker trap is treating 开口 as a synonym for 说. It is not. 开口 has no object of its own, so you cannot say 开口这件事. If you want to say what was said, 开口 stays intransitive and 说 does the carrying: 他开口说了几句话. Use 开口 for the threshold and 说 for the content.