The correct answer is B. He said that he is writing a poem.
The sentence “He said, ‘I am writing a poem'” is in the direct form. In the direct form, the words spoken are quoted exactly. The indirect form is used to report what someone said without quoting their exact words. In the indirect form, the verb “say” is used with a different tense, and the pronouns may be changed.
In this case, the direct form is “He said, ‘I am writing a poem.'” The indirect form would be “He said that he is writing a poem.”
The other options are incorrect because they do not accurately report what the speaker said. Option A, “He said that I am writing a poem,” changes the pronoun from “he” to “I.” Option C, “He said that the poem is being written,” changes the tense of the verb from “is writing” to “is being written.” Option D, “He said that he was writing a poem,” changes the tense of the verb from “is writing” to “was writing.”