When your boss or another employee asks you to get a project back to them quickly and efficiently I think “quick” takes too much dominance. Hearing “quick” makes you think you need to rush the finished product right back to them, but I do not think it is right to assume that “quick” is the more important word here.
What good is a project that is returned quickly but not done properly? In the end won’t it take more time to go back and correct mistakes?
I think the word that deserves more focus is “efficiently”. Do the job properly and show some pride in your work. Even if it’s a small job like making copies, do it right and make it presentable. You will present yourself as a diligent worker who can work in a promptly manner.
Ask questions so you know exactly what is expected in the final product. Take your time to make sure there are no mistakes. Think about how you want to present the completed project in an organized fashion. These little details demonstrate the skills you would have if you were to continue working for that company. Do the little things will care and earn the trust to be delegated bigger tasks.