How i write leave application of brother's engagement?

Just like you would for anything else. Of course, the specifics of your application will depend on what you’re asking leave from (school, work, etc.) and how formal they expect your request to be. In any case, you should start with a greeting, list the date(s) you’ll need to be away, and explain why you need to be out. As long as you keep it respectful and honest, you can’t go wrong.