Hearing someone out means listening to what a person has to say even if you don't want to. You may not agree with the ideas; you may think they are stupid or ridiculous, but if the person wants you to hear him out, he just wants you to listen and to give him and his ideas a chance.
As you can probably imagine, sometimes people say this out of frustration as when someone disagrees with you so strongly that he or she is no longer open to anything you have to say. If you really want this person to listen, you say, "Just hear me out." Then you speak your mind.
1. I know you don't agree with this, but just hear me out. I think I have some good ideas.
2. We strongly suggest you hear out what your lawyer has to say. It's your only hope.
3. I know; you're angry with them, but let's just hear them out. They might be able to give us some clues as to what exactly happened.
4. Please just hear us out, and if you still want to call the police, there's nothing we can do.
5. We agree with you; she's nuts. But let's just hear her out. You never know; she may actually know a better route.
Alright, I know most of you don't like repetition when it comes to practicing English, but just hear me out. Rereading old exercises over and over is an excellent way to get more comfortable with English and improve your language skills. So get to it.