Which of the following is NOT a way to illegally influence a coal mine worker's response to an inspector?

Providing additional training to a coal mine worker is not a way to illegally influence their response to an inspector. In the context of workplace regulations, training is generally viewed as a constructive and positive action aimed at improving safety, compliance, and competency among workers. It fosters an environment where employees are better prepared to handle their responsibilities, including interactions with inspectors.

In contrast, the other options involve coercive or manipulative tactics that could undermine the integrity of an inspection process. Promising a promotion, issuing general directions that pressure or indirectly influence the worker's responses, and threatening dismissal create an environment of fear or expectation that could sway a worker's honesty or willingness to report issues accurately. Such actions are considered forms of illegal influence as they can distort the truth and compromise safety protocols, which are specifically designed to protect workers and ensure compliance with regulations.