It's worth noting that Zero Hour is a standalone expansion to Command & Conquer: Generals. If you can find a copy of the original game or purchase it, you might be able to find a free or cheap version of Zero Hour.
While there isn't a straightforward way to download Command & Conquer: Generals Zero Hour for free, there are still some options to consider. You can check the Origin platform, look into the Command & Conquer: Remastered, or keep an eye on digital stores and online communities for potential deals or giveaways.
GOG (formerly Good Old Games) sometimes offers free games, but Command & Conquer: Generals Zero Hour is not currently one of them. You can, however, purchase the game or the Command & Conquer: Generals Collection, which includes Zero Hour.
EA offers a free trial for some of their games, but it's unclear if Command & Conquer: Generals Zero Hour is one of them. You can check the Origin website for more information.