Step 1: Sentence Construction
The sentence employs a conditional clause initiated by "Had he," signifying the subjunctive mood.
Step 2: Appropriate Verb Tense
Following "Had he," the past participle "known" is mandatory for constructing the past perfect subjunctive.
Step 3: Evaluation of Alternatives
- "knew" represents the simple past, which is unsuitable in this context.
- "knows" denotes the present tense, rendering it incorrect.
- "knowing" functions as a gerund or participle, making it inappropriate.
Outcome:
The correct construction is "Had he known."