Final answer:
The Electronic Stability Program (ESP) system applies the brake to the front wheel on the opposite side of the skid during a rear-wheel lock-up to counteract over-steering and regain vehicle control.
Step-by-step explanation:
During an over-steering or skidding condition, specifically with rear-wheel lock-up, the Electronic Stability Program (ESP) system intervenes by applying the brakes to the front wheel on the opposite side of the skid. For instance, if the rear end of the car is skidding to the left, the ESP will apply the brake to the front right wheel. This action helps to counteract the skid and brings the vehicle back to the intended direction of travel. It is part of the vehicle's advanced safety features, intended to enhance handling and prevent loss of control.