The textbook is right, a is more appropriate. All the context necessary is given in the screenshot, the person who said the sentence is a newsreader.
The difference is subtle. The newsreader is reporting something that will definitely happen in the future. It is a statement of fact. It will happen, no ifs, no buts, no maybes. Do you see the difference?
If you use 'going to', although we understand as a listener it is highly likely that the said event is going to happen, it leaves open the possibility (however small it might be) that it is open to change. The King should arrive at 6, that is what is scheduled to happen. That is what we understand. But A leaves no leeway, no wiggle room which B does. For that reason B sounds weird in the context provided.