Eukaryotes are the organisms that possess a true nucleus (containing the DNA, which is the genetic material) and the membrane bound subcellular compartments ( also known as cell organelles) such as golgi complex, endoplasmic reticulum, mitochondria.
As per the given information in the question, cells of mushrooms, plants, and animals all have visible nuclei under a microscope.
Thus, it indicates that these organisms are eukaryotes.
