The correct answer is: D. No correction required.
The sentence “When I get home, my children would be playing” is in the future perfect continuous tense. This tense is used to talk about an action that will be in progress at a specific time in the future. In this case, the speaker is saying that their children will be playing when they get home.
The other options are incorrect because they do not accurately reflect the meaning of the sentence. Option A, “would have been,” is in the past perfect tense. This tense is used to talk about an action that was completed before a specific time in the past. In this case, the speaker is not saying that their children were playing before they got home. Option B, “will be,” is in the simple future tense. This tense is used to talk about an action that will happen at a specific time in the future. In this case,
the speaker is not saying that their children will start playing when they get home. Option C, “have been,” is in the past perfect continuous tense. This tense is used to talk about an action that was in progress at a specific time in the past. In this case, the speaker is not saying that their children were playing at a specific time in the past.