Explain the differences between the Federalists and Anti-Federalists. Why did the Anti-Federalists want a bill of rights? Explain how this country would have been different had they not been successful in their push to add a bill of rights.

The thing to keep in mind, when you look at the Federalist Debates, is that they existed within the context of the Constitution's ratification. When we look back at those debates, we see it with the benefit of over 200 years of perspective. The Framers were living before in a time when democracy was still very much unproven, and no one could know whether a democratic government could be successful or if it would end in failure. That detail is critical to understanding the entire debate.
Additionally, you also need to recognize that the Constitution was not the first system of government envisioned for the United States. Earlier, there had been the Articles of Confederation, which envisioned a much more decentralized system of politics, with far greater power situated with the individual States. However, that system struggled to deal with the political realities of an independent United States. To address the shortcoming of the Articles of Confederation, the Framers of the Constitution placed far more power and authority with the Federal Government.
That is the historical context behind this occasion. The Federalists and anti-Federalists took competing positions in a debate, one side defending the Constitution and championing its ratification, and the other side seeking to defeat it. Your first task is to identify which position was taken by the Federalists and the anti-Federalists, and consider the arguments marshaled by each side. Ultimately, what were they concerned with? Why did they hold these assumptions?
From here, we get to the Bill of Rights, and here the basic core question you need to consider is this: what is the fundamental purpose of the Bill of Rights? Consider what kind of provisions are contained in the Bill of Rights, and think about those provisions in the context of the Federalist Debates already discussed. At the same time, I'd suggest you consider more modern history. There have been a lot of debates surrounding political rights, as well as the infringement of those rights. Now, imagine a world which does not have a Bill of Rights to begin with. What might this hypothetical United States look like? In answering that hypothetical question, you should have the answer to the last of these questions.