High schoolers who brazenly smoke in the classroom, and teachers who can't correct them, will both be punished.

Literal

Classroom [at-で] brazenly tobacco [object-を] smoke high-schoolers [and-と] that [object-を] cannot-correct teachers [topic-は] punishment [object-を] receive [thing-こと] [will-become-になります].

School policy announcement. どうどうと ('brazenly, openly, without shame') is a mimetic-adverbial for unashamed, bold behavior. 注意する ('to correct, to admonish, to warn') is the standard verb for a teacher's corrective intervention. ~ことになる ('it will come to pass that X, be decided that X') marks an administrative/consequential outcome. Both the students and the teachers are the subject of punishment — interesting dual accountability.