Step 1: Sentence structure
The sentence uses a conditional phrase starting with "Had he," which is a subjunctive form.
Step 2: Correct verb form
After "Had he," the past participle "known" is required to form the past perfect subjunctive.
Step 3: Verify other options
- "knew" is simple past, incorrect here.
- "knows" is present tense, incorrect.
- "knowing" is gerund/participle, incorrect.
Conclusion:
The correct form is "Had he known."