Great example. A few tips for you:

We don’t typically say “know-how about”. We usually say “know-how to” + a verb. I would edit in the following ways:

In the first example, I would say, “…countries didn’t have the know-how to distribute and administer the vaccine.”

In the second, keep in mind “know-how” is something you either have or you don’t. I wouldn’t describe it as “huge” or “small.” It’s either yes or no. So you can simply say, “But Brazil had the know-how to manage this process.”