They said to him, “We shall visit your house tomorrow”.

They said that they will go to his house the next day.
They expressed a desire to visit his house the next day.
They told him that they might visit his house the next day.
They told him that they would visit his house the next day.

The correct answer is D. They told him that they would visit his house the next day.

The sentence “They said to him, ‘We shall visit your house tomorrow'” is a direct statement of intent. The use of the word “shall” indicates that the speaker is making a promise or commitment to visit the listener’s house on the following day. The other options are incorrect because they do not convey the same level of certainty or commitment.

Option A is incorrect because it uses the word “will,” which is a less formal and less certain way of expressing intent. Option B is incorrect because it uses the word “desire,” which suggests that the speaker is not sure whether or not they will actually visit the listener’s house. Option C is incorrect because it uses the word “might,” which suggests that the speaker is only considering visiting the listener’s house and has not made a firm decision.