By~ing, Of~ing

"Marketing" is a company's department responsible for letting people know about its products, encouraging them to buy those products though advertising.

"Of trying to get people to buy your products by, for example, having advertising," is another item describing what "marketing" is. It is not explaining what "marketing is," which would be the case if you were to say, "by trying to get people to buy your products by, for example, having advertising."

By the way, you don't need the comma between "business" and "responsible."

Thank you so much!

That means that I can say "Marketing is the area of trying to get people to buy your products by having advertising." Am I right?

It would be better to omit the word "having."

Better yet would be the substitution of the word "by" with the word "through."