Okay kiddo, let me explain the transnational capitalist class to you like you're five.
You know how there are people who have a lot of money and they use that money to buy things they want and need? Well, sometimes those people own big businesses that make even more money. And sometimes those businesses are so big and powerful that they do business in many different countries, not just one.
When businesses do business in many different countries, they become what we call "transnational." And when the really rich people who own those businesses work together to make even more money, we call them the "transnational capitalist class."
These people are really powerful because they control a lot of money and they use that money to make even more money. They also have a lot of influence on politics and the way the world works.
So in short, the transnational capitalist class is a group of very rich and powerful people who own big companies that do business all around the world. They work together to make even more money and they have a lot of influence on how the world works.