The correct passive voice of the given sentence is A letter was being written by Rahim.

The active voice of the sentence is Rahim was writing a letter. This sentence is in the simple past progressive tense, which is used to describe an action that was happening in the past and was continuing at a certain point in time. The passive voice of the sentence is formed by putting the subject of the active sentence after the verb "to be" and the past participle of the main verb. In this case, the subject of the active sentence is "Rahim" and the main verb is "write." The past participle of "write" is "written." So, the passive form of the sentence is A letter was being written by Rahim.

The other options are incorrect because:

• A letter was written by Rahim. is in the simple past tense, while the original sentence is in the simple past progressive tense.
• Rahim had been writing a letter. is in the past perfect progressive tense, while the original sentence is in the simple past progressive tense.
• A letter did Rahim write. is in the active voice, not the passive voice.
• A letter being written by Rahim. is not a complete sentence. It lacks a verb.