Final answer:
The most likely coping style adopted when a stressor is appraised as high demand but there are sufficient resources to handle it would be problem-focused coping, which aims to address the problem directly.
Step-by-step explanation:
If an individual's primary appraisal of a stressor determines it to be of high demand, yet their secondary appraisal recognizes they have sufficient resources to manage it, the most likely coping style to be adopted is problem-focused coping. This approach involves actively trying to manage or alter the problem causing stress, as described by Lazarus and Folkman (1984). This form of coping is typically applied when an individual perceives the stressor as controllable and believes they possess the abilities and means to deal with it effectively. It entails strategies such as planning, seeking information, and taking direct action to confront the issue at hand.
On the other hand, the emotion-focused coping style is often adopted when a person appraises a stressor as uncontrollable or insurmountable, focusing instead on managing the emotional distress associated with it. Given the sufficient resources identified in the secondary appraisal, a problem-focused coping style is the likely path for someone in this scenario to minimize stress and manage the situation proactively.