In the sentence Henry’s desire to (graduate) is obvious the correct option is B. infinitive. It is a verb preceeded by the prepositon to that forms the full infinitive.
itn the sentence (Running) is not allowed in the hallways the correcto option is A: gerund. A gerund is a verb form (adding -ing to a verb) that functions as a noun
The early difficulties of Elizabeth's reign secured him a deceitful peace on that side for a time
I see what you are trying to ask, but a piece of writing can contain more than one organizational structure.
For example, The school district is making it hard for students to eat poorly