• adhikṣiptaḥ — insulted
  adhi + √kṣip, 'to throw at.' A specific kind of insult — words 'thrown at' someone, more violent than mere avamāna. Names what passes the threshold of Balarāma's tolerance.
• kruddhaḥ — angered
  From √krudh. Distinguished from manyu (verse 31): manyu is sustained, krodha is the flash. Balarāma's manyu (slow swell) ripens into krodha (the strike). The Bhāgavata's emotion-vocabulary is exact.
• parigham — His club
  Sanskrit for an iron-bound club, a heavy bludgeon. Distinct from Balarāma's signature musala and hala. The Bhāgavata varies the weapon-name in verse 38 too — pariga(ha) suggests an improvised wedding-hall weapon, perhaps a door-bar.
• jaghne — He struck dead
  From √han. The same root as in Hanumān ('struck-jaw') and ahiṁsā. Bhāgavata uses jaghne for fatal blows by Bhagavān and His expansions only — never for ordinary killings.
• nṛmṇa-saṁsadi — in the auspicious assembly
  nṛmṇa (auspicious, joyful) + saṁsad (assembly). The verse's bitter irony: the killing happens in the very assembly called 'auspicious.' Bhāgavata's narrative knife — the word for joy holds the corpse.

• How often do I take divine patience as permission to keep offending?
• Where is my own tolerance being mistaken for endless indulgence?

Like a club falling at last on the rim that has cracked under many small blows, the parigha rises and falls in the wedding-hall — and the same auspicious assembly that gathered to bless a marriage becomes the scene where Saṅkarṣaṇa, who draws together, draws Rukmī's life away.