Ответ:
Mike said that He liked that story.
Mike said thet He would go Moscow the next day.
Mike said that He was sleeping then.
Mike said that Mother had cooked a cake.
Mike said that He had built that house. (Ты наверное ошибся, вместо Had - has)
Mike said that He was going to play chess then.
Mike said that He did his homework every day.
Mike said that He could play the piano.
Mary asked me If I spoke French.
Mary asked me If I had seen him the day before.
Mary asked me what I was doing then.
Mary asked me when I had gone to Parish.
Mother told Ann helped her.
Mother told children didn't be noisy.
Mother told Mary washed up, please.
Mother told Bob didn't water the flower.
Mother told Mike did the homework.