Mix soy sauce, water, honey, and cornstarch in a small bowl; set aside.
Heat oil in a wok or large skillet. Add minced garlic; sauté about one minute until garlic is golden.
Add chicken; cook about 5-6 minutes, then push chicken to the side.
Add onions to center of skillet; cook until slightly tender and push to the side. Continue with carrots, broccoli, and peppers separately, placing each in the center of pan, cooking until slightly tender and pushing to the side.
Pour soy sauce mixture into center of skillet. Leaving other ingredients at the sides of the pan, stir sauce until it thickens. Mix in with vegetables and chicken.