Let it (i.e. what he feels about the state) be written on the forehead of each person.A passive verb doesn't have a direct object. The direct object becomes the subject.
Hoc scribam = I will write this (active; hoc is the object).
Hoc scribetur = This will be written (passive; hoc is the subject).
assuming that this is correct; that “it” is defined by what is inside the parenthesis, and that “it” is also the subject of the passive verb “written”; is there a clue to how quid is being used in the sentence (as “what” in the phrase “what he feels about the state”), or is it just intuitive? [does this phrase have a technical name that I could look up and see examples?]