Heat olive oil in a skillet over medium heat. Stir red bell pepper and garlic into hot oil; season with salt and black pepper. Cook and stir until the bell pepper is tender, 5 to 7 minutes.
Stir green beans with the red bell pepper. Pour white wine over the green bean mixture. Place a cover on the skillet and cook until the green beans are tender, about 10 minutes.
Stir the green bean mixture. Sprinkle feta cheese over the mixture. Replace cover and continue cooking until the feta softens, about 3 minutes.
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