The correct passive form of the given sentence is:

☀ The latest assignment was explained to Lana by the manager.

So, the correct passive form is: "The latest assignment was explained to Lana by the manager."

The other options and their explanations:

☀ The latest assignment had explained to Lana by the manager.

• This option is not grammatically correct. In the passive voice, the past participle form of the verb ("explained") should be used, not the base form ("explain").

☀ The latest assignment had been explained to Lana by the manager.

• This option uses the correct past participle form ("had been explained"), but it introduces a past perfect tense, which does not match the simple past tense of the original sentence.

☀ The latest assignment had been explain to Lana by the manage.

• This option contains a grammatical error. The correct form is "explained" (past participle) instead of "explain" (base form), and "manager" is misspelled as "manage."