Think Th2: wherever you see eosinophils plus IgE plus allergy, the cytokine family at work is IL-4, IL-5, and IL-13 from Th2 cells.
Cross out the rest: IL-2 is the T-cell growth factor, it expands lymphocytes not eosinophils. IL-1 and IL-6 are classic macrophage-derived pyrogens that cause fever and acute-phase response but have no specific eosinophil role.
Pick within the list: the most specific eosinophil cytokine is IL-5, yet it is absent from the options. IL-4 is the master switch that commits naive T cells to the Th2 lineage, so it sits at the top of the pathway that produces eosinophilia. Therefore IL-4 is the best available answer.
Pearl: remember IL-4 starts Th2, IL-5 grows eosinophils; when only IL-4 is offered, choose it.
Reference: basic immunology, T-helper subsets.