It's "do business". I'm not sure why your teacher corrected you.

I am a native American English speaker and I would say "I do business with several companies in New York.", not "I make business with several companies in New York." The only place I can think of offhand where the words "make" and "business" come together are in sentences like: 1. I will make business cards for my company this weekend. 2. They will make a business out of selling clothing for pets. Do you remember any of the examples that your teacher gave you? If so, post them here and I will let you know if they sound unnatural in American English.

"Do business" is correct.

I agree with the others - do business. The only thing to be careful of is not to say 'do MY business'. In British English, this means go to the toilet.

As someone who holds an MBA (Master of Business Administration) degree, I can tell you with absolute certainty that it is "do business."