Prepare the Teriyaki Sauce: Whisk the crushed garlic, dried ginger, soy sauce, water, apple cider vinegar, and sugar together in a measuring cup until combined. Set the sauce aside.
Prepare the Chicken and Vegetables: Chop the onion, dice the carrot, cut the zucchini into matchsticks, and slice the chicken breasts into strips. Season the chicken with 1/2 teaspoon salt and 1 teaspoon pepper.
Heat the Wok: Place a large wok or skillet over high heat until hot, then add the oil and allow it to heat.
Stir-Fry the Vegetables: Add the prepared onion, carrot, and zucchini to the hot oil and stir-fry over high heat for 3 minutes. Remove the vegetables from the wok and set them aside.
Cook the Chicken: Add the seasoned chicken strips to the same wok and cook over high heat for 5 minutes, stirring occasionally. Remove the cooked chicken and set it aside.
Scramble the Eggs: Add 1/4 cup oil to the wok, then crack in the 2 eggs. Scramble the eggs while chopping them into smaller pieces with the spatula.
Fry the Rice: Stir the cooked rice into the scrambled eggs and fry over high heat for 3 minutes, stirring as needed to combine everything.
Add the Teriyaki Sauce: Pour the prepared teriyaki sauce into the fried rice and stir thoroughly so the sauce coats the rice.
Combine Everything: Return the sautéed vegetables and cooked chicken to the wok, then stir-fry until the chicken, vegetables, rice, eggs, and sauce are evenly incorporated.
Serve: Serve the teriyaki chicken fried rice while hot, optionally accompanied by yum yum sauce or homemade ranch dressing.