Answer:
He does not want to encounter the disgraces of the husband of a faithless woman. But it may also be for other reasons. He does not want to hear all the talk about his wife being unfaithful.
Step-by-step explanation:
I shall read (the letter of infamy) on his heart"? ... The human eye refers to that of the father of the child, Arthur Dimmesdale. Hester sins anew (again) by continuing to love / want him.
Hope that helps :)