The correct passive form of the given sentence is:

☀ Her day is begun with a cup of coffee.

Let's break down the options:

1. Her day is being begun with a cup of coffee. (Incorrect) While this sentence is in the passive voice, it uses the present continuous tense ("is being begun"), which doesn't fit the original meaning. The original sentence talks about a habitual action ("begins her day"), and the passive form should also reflect that with the simple present tense ("is begun").

2. Her day is begun with a cup of coffee. (Correct) This sentence correctly uses the passive voice and conveys the same meaning as the original sentence.

3. A cup of coffee Is beginning her day. (Incorrect) This sentence is in the active voice and does not properly reflect the passive form of the original sentence.

4. A cup of coffee has begun her day. (Incorrect) This sentence is in the active voice and suggests that "a cup of coffee" is the one actively starting her day, which is not the intended meaning of the original sentence. The passive form should focus on "her day" being begun by someone or something else (in this case, by the action of starting with a cup of coffee).