Answer: The professor asked Gloria Pritchett and me to give a guest lecture at the university.
Step-by-step explanation:
When taking about another person and yourself, you would a say their name first, and then “I” to refer to yourself if you and that person are the subject, the main focus of the sentence, An example of this would be Sally and I went to the theme park, because Sally and yourself are the ones enjoying or doing the verb.If you are talking about another and yourself, but that other and you are the object or verb, the background of the sentence, use Sally and me. An example of this used correctly would be Jeramy explained the process of making caramel to Sally and me. Jeramy is the subject of the sentence, not Sally and yourself.
I hope this helps!