The example of a government where both the president and prime minister are active participants in the day-to-day administration of the state is typically found in a semi-presidential system. An example of such a nation is France, where both the president and the prime minister play significant roles in government operations.
From the options you provided, it appears they are coded responses rather than countries, so I can't identify a specific nation without more context. If you are looking for a specific country among those options, I would recommend checking which one corresponds to a semi-presidential system. If you can provide more details or clarify the options, I would be glad to assist you further!