You realize that the headline and the actual text have opposite meanings, right? In the headline, you're asking, it seems, whether brutal dictatorships supported the US, and in the text, you're saying that the US supported them, so it's hard to tell what you're looking for help on.
That said, I might guess that you're writing an essay on the second version--whether the US supported brutal dictatorships. You're dealing with loaded ideas here and loaded language as well, so a simple "yes" or "no" won't be enough; whichever answer you pick, you'll have to defend it from people who strongly disagree.
Here's how you might get started:
Assume for a moment that the answer is yes, the US has supported brutal dictatorships in the name of freedom. What examples stand out as most obvious? You might use these to define your terms. How do you know it's a dictatorship? How do you know it's brutal? How did the US support it? How do you know it was "in the name of freedom?"
Now switch sides. Who might disagree with you? On what basis would they disagree? Do they disagree with your definitions? Do they disagree with the implication of American hypocrisy? Do they disagree on the facts themselves? I.e., do they simply not believe that the US supported them?
Now look at the two sides. Which argument do you think is stronger? What makes it stronger?
Hope this helps--let me know if you'd actually like to work on it together!