In another skillet, melt butter over med-high heat. When melted add the green beans and saute them for about 4 minutes, turning the beans a few times. You want the beans to still have a "crisp" bite to them so be sure to not to over cook them.
Add the walnuts and heat through, about 1 minute, then add the garlic and cook 1 more minute, stirring to prevent the garlic from burning.
Turn off heat, and add the balsamic vinegar, toss the beans and walnuts to coat with the vinegar.