Prevent File Sharing

You cant I'm afraid - everything on the internet (not just Dropbox) is shareable if they have the link. So, the only way to stop it is to make sure the other person doesnt pass it on.

You could add passwords etc. to the link or file, but, that doesnt stop the other person sending it.

You could also put it in a Shared Folder and restrict sharing on the folder, but, the other person just needs to make a copy of the file and they can share that. Or, even if you do all of the above the first person could quite easily download the file and reshare it without you knowing via a shared link they make.

You need a Professional or Business account in order to set a password or expiration on a share link. Remember, in addition to what Mark has stated above, there's nothing stopping a person from sharing not only your link, but the password for that link as well.

As soon as you share something with someone else, you lose total control of it. That's nothing to do with Dropbox. It's just a fact of sharing, on any platform.