Say you think the government is pressuring bookstores to take your book off their shelves. You want to get an injunction ordering the government to stop doing that. You acknowledge that the bookstores didn't violate the First Amendment, because the First Amendment doesn't bind the bookstores themselves. But you're arguing that the government violated the First Amendment by pressuring bookstores this way.
To get the injunction, you'd generally need to show four things (to oversimplify somewhat):
- Traceability of past injuries: The bookstores have in the past taken your books off the shelves because of government pressure and not just because they concluded on their own that they didn't want to carry the books after all.
- Substantial risk of future injury: The government is likely to act in a way that injures you in the future (since you're seeking an injunction against future action).
- Redressability: Issuing the injunction in this case is likely to prevent the harm, because the bookstores—freed from the government pressure—are likely to keep your books on the shelves.
- Merits: The governmental pressure indeed violates the First Amendment, for instance because it coerces the bookstores rather than just persuading them.