"To have somebody do something" means that you ask or pay for someone to do something for you. It means I asked the doctor to examine my eyes. This expression is more common in American English. In the UK we might say, "I had my eyes examined by the doctor' This causative has the form "To have something done"

It refers to a medical examination of the eyes. In other words, you are having your doctor check them for possible health problems. Since it's causative form, you are not checking your own eyes, but "causing" the doctor to do it for you.

*I'm going to keep trying... ("I gonna" is laughably poor English.)

Thank you to everyone for helping me. I know that to learn another language is also necessary to understand their culture. However, when you don´t have a direct contact, the case of such an exchange, becomes more difficult. But I won´t give up. I gonna keep trying until I get it.

You caused the doctor to perform an examination probably by scheduling an appointment. My concern is not with your question but with your explanation. You found something that caused you to be confused. The statement confused you. Don't worry. We all get confused. The question "may anyone" is a awkward. Make a request. Please help me understand how this sentence is causitive. Ask how the sentence shows causation?