Correct answer (among the given options): IL-4.
Step 1: Tissue and blood eosinophilia, as in this eosinophilic myositis, is driven by the Th2 cytokine arm. Th2 cells secrete IL-4, IL-5, and IL-13.
Step 2: IL-4 is the master Th2 cytokine: it drives Th2 differentiation and the eosinophilic, IgE-rich allergic response. (Note for completeness: IL-5 is the most specific cytokine for eosinophil growth and recruitment, but IL-5 is not offered here, so IL-4, the Th2 driver, is the intended answer.)
Step 3: Why not the others. IL-2 drives T-cell proliferation. IL-1 and IL-6 are pro-inflammatory pyrogens from macrophages and do not specifically expand eosinophils.
Ref: immunology of Th2 responses, Robbins.