How do large food particles enter the amoeba?

The answer is: by the process of phagocytosis.

Large food particles enter the amoeba through a process called phagocytosis. During this process, the amoeba's organelles and vacuoles contain and store food molecules. In addition, the amoeba is protected by an elastic membrane, which allows gases to pass through while also containing a cellular mucus. Some food particles are too large to be transported, so they are taken up by the amoeba through phagocytosis. This process allows the amoeba to consume large food particles and obtain nourishment from them.