Based on what is depicted, the father is engaged in a discreet encounter. The son enters the scene, distracted by a phone call, which I assume is with the mother. He walks down the hallway, appearing unaware, and goes to his father's location, which appears to be his study. The son is likely under the impression that his father is occupied with work.
The father's comment, 'and that would be my undoing,' suggests that the potential discovery of this situation would have significant negative consequences for him.
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