This is an exam question, so the author is free to assume whatever he wants. But, more importantly, the interaction as large as half of the main effect is alre

This is an exam question, so the author is free to assume whatever he wants. But, more importantly, the interaction as large as half of the main effect is already pretty large -- in real world, many studies look at much smaller interactions. The point here is that if you need 16 times sample size to get enough power to detect the interaction at half effect size, you will need even larger sample size to detect smaller interactions.