When someone is busy, it is important to take some time to organize and prioritize the work. Many people just try to work faster, but that doesn't really help. Planning and working smarter is the best answer when times get busy.
You can answer by saying that you will work harder or work faster or even work overtime, but people with experience knows that working smarter by planning and organizing comes from experience. So even if you don't have much experience, this type of answer can make you look like you have been in this type of position many times and overcame them.