How is per hour billing working for most of providers? if I have a server created a VPS, used 4 hours, and shutdown for the rest of day without deleting the server. Does that count for 4 hours, or 24 hours since the VPS is still there, even though it is not running?

You'll probably find pricing based on parameters such as compute power, storage usage and bandwidth consumption. Some providers clearly define each resource utilization and others will mask some of this to make billing simpler to understand. The resources have to be accounted for in some manner but how the provider presents that to you is up to them. With that said, how the cost is passed onto you varies greatly depending on which provider you use.

Most providers do charge even when the VPS is suspended or shutdown. System resources need to be reserved for the VPS even when it is shutdown so that they are available when the VPS is powered on.