Beth learned in her science class that white blood cells in the human body capture harmful material by engulfing them. then they digest them using enzymes, thus protecting the body from infection. which eukaryote has a similar mode of nutrition?

The eukaryote that has a similar mode of nutrition to that of the white blood cells is AMOEBA.
Amoeba feed on microscopic organisms. When amoeba encounter a food particle, it extends its pseudopodia around the food particle and ingest it. The food particle which is now in the food vacuole of amoeba is broken down and digested by mean of digesting enzymes secreted by the organism.