I'm not sure what you are asking. An internal conflict is one that a character has within himself. So an internal conflict would be one that Charlie has to deal with himself, such as his struggle against his loneliness. Perhaps you mean an external conflict that Charlie has with someone else or something else in the story. One external conflict he has is trying to fit in society. He still doesn't fit in even after he becomes a genius, and he's still lonely.

What was one external conflict Charlie Gordon had in the book?

In harmony with the above comments, Charlie struggled with fitting in: when he lacked intelligence he always allowed things to happen to himself in order to amuse Joe, Frank, et al and as his intelligence increased he had trouble fitting in with those who weren't as smart as he had become especially Ms. Kinnian because he would talk about concertos, math, and many languages and those less intelligent people were unable to comprehend. So on both ends of the spectrum Charlie struggled with acceptance.

What was one external conflict Charlie Gordon had in the book?

Another external conflict that Charlie had to deal with was his relationships with the people at work.  At the beginning of the story, they are cruel to Charlie and take advantage of him to amuse themselves.  Later as his intelligence level grows he realizes their cruelty and their relationship begins to change.  As he reaches the height of his intelligence, they begin to fear him and try to get hm fired.  Only one does not sign and she sees that something is not right with Charlie and wants him to return to the "good simple man" he was.  Later when he is losing his intelligence and goes back to work in the bakery, the workers accept him back and are kinder to him than they were before.  Charlie has also come to terms with their making fun of them remembering that they were never as intelligent as he once was.

What was one external conflict Charlie Gordon had in the book?

Charlie has to withstand abuse by his mother as a child. She at first wouldn't accept that he had limited intelligence, and when she finally did, she was afraid he'd hurt his sister. As an adult, Charlie has to deal with the people who make fun of him and abuse him. Even before his operation, Charlie knows who is kind to him and who isn't. He mainly wants people to treat him like a human being, no matter what.