Winston reads from Goldstein's book that "The invention of print, however, made it easier to manipulate opinion." Explore the history of using print to influence opinion—and not just propaganda.

This seems to be less an essay about "1984" and more about history. With this in mind, there are several questions you'd need to ask. Most notably: does printing impact public opinion. After answering this question, the next question is how, and why? If your answer is a simple and straightforward one, perhaps you could think about ways to complicate it provide nuance? For example, take "1984" itself: the quotation provided here actually forms part of a more complicated thesis. "The invention of print, however, made it easier to manipulate public opinion, and the film and radio carried the process further," and according to Goldstein, television took it even further than that. Orwell couches his analysis as a kind of process, by which the tools and technology the State uses to control and manipulate opinion is something which is built and intensified across time, from one era to the next. Of course, it needs to be stated: yours is actually a different question than the one Orwell's asking, but this example does show how to create a more complex approach to these kinds of answers. It's not always a matter of yes, it does, or no, it does not.
With this in mind, think about the ways that print has been used to influence opinion, but also think about how the answer to this question might have changed over time. Think about the people who have shaped opinion, as well as the people who they are addressing. Furthermore, would you consider the print's power of influence a positive or negative, or does this answer depend solely on the specificities of each case you are discussing? You can discuss the use of pamphlets, of books, and of newspapers. You can discuss government based initiatives as well as private organizations. You can discuss how print is used in wars, in periods of political turmoil, and you can even think in terms of consumerism and advertisements, or in terms of the sciences and academia (think about the conversations and disputes that have been held within the scientific or philosophical communities).
Moreover, in answering these questions, you should aim to think historically: think in terms of how much things have changed over time, in terms of technology and culture, as well as what has remained constant. Indeed, this is perhaps one of the most important themes of all, given how this question specifically asks you to "explore the history of using print to influence public opinion." You need to look at this question from a more long term, big-picture viewpoint, and consider how the relation between print and opinion has evolved over time. What has remained constant, what's changed, and what examples can you find which illustrate the pattern you've observed?
Finally, be aware: the question notes specifically that it is asking for more than just examples of "propaganda." Be aware of this, and plan accordingly.