How do I change 'He said, "I am writing a letter"' into indirect speech?

Follow four steps. First, the reporting verb 'said' becomes 'said that' (drop the inverted commas and comma, add 'that'). Second, shift the tense one step back: present continuous 'am writing' becomes past continuous 'was writing'. Third, change pronouns to match the speaker: 'I' refers to 'He', so it becomes 'he'. Fourth, keep the rest unchanged here. The correct sentence is: He said that he was writing a letter. Remember the pronoun rule of thumb: first person follows the subject of the reporting verb, second person follows the object, and third person stays the same. Always check the tense shift, because that is where most marks are lost in the SSC exam.