Let's analyze each option:

☀ The doctor said that everyone in this room might wear the face mask.

This option changes the tense and introduces the modal verb "might," which implies a possibility rather than a definite requirement. It does not accurately represent the original sentence's meaning.

☀ The doctor said that everyone in this room might worn the face mask.

This option contains a grammatical error. "Might worn" is not a correct verb form. The correct passive form of "wear" is "be worn."

☀ The doctor says that everyone in this room must wear the face mask.

This option changes the tense to present, but it is in the active voice. The original sentence is in the reported speech, and the requested form is the passive voice.

☀ The doctor said that everyone in this room must wear the face mask.

This option correctly represents the original sentence in the reported speech and the passive voice. The passive form of the original sentence is: "The face mask must be worn by everyone in this room."

Correct answer: ☀ The doctor said that everyone in this room must wear the face mask.