Barely had Jack reached the place ____ Jim started arguing with him.

Hardly, scarcely and barely are followed by when ; while no sooner is followed by than.
Example:
- Barely had they won the match when the coach had a heart attack. 
- Hardly had I arrived home when my phone rang. 
- Scarcely had she finished reading when she fell asleep.

বাক্যের শুরুতে hardly, rarely, barely, seldom, scarcely থাকলে inversion (auxiliary verb + subject + main verb) হয়।