What is the grammatical name of this expression 'that he would agree to run the state' and what is it function​

to eliminate ambiguous remote or broad reference it is necessary to focus on anaphoric reference. by definition "anaphoric reference means that a word in a text refers back to other ideas in the text for its meaning." the references should be clear and leave no room for ambiguity.

in the first case the pronoun it probably refers to the car but it has not been mentioned before so we should replace it for the car. in doing so the statement becomes clear.

in sentence number   two   the pronoun he refers to charles dickens the author. yet, the first half of the sentence is about the book a tale of two cities. to repair this it would be better to rephrase the first half : after i read   a tale of two cities by dickens, he so as to remove the remote reference.

as much cookies cookie monster could muster if a cookie monster could master cooking cookies