He caused a scene while drunk and disgraced the company.
Tips
memory
Literally 'to smear black onto [someone's] face'. In Chinese, 'face' (lian) is reputation; smearing it black is the visual metaphor for shaming someone publicly. The image carries directly into the meaning.
grammar
Pattern is 往 + [target's] 脸上抹黑. The 往…上 frame works generally for 'apply X onto Y': 往墙上抹油漆 ('smear paint on the wall'), 往身上喷香水 ('spray perfume on oneself').
