What are we going to have at the end of June?
When are we going to have our examination?
How many hours a day do I intend to spend on my English before the examination?
What do I intend to spend three to four hours a day on before the examination?
When do I intend to spend three to four hours a day on my English?
Если задание из Бонка, то там подчеркнуто еще местоимение I. Тогда 4й вопрос к подлежащему:
Who intends to spend three to four hours a day on English before the examination?