The man who sat next to me reeked so much of whiskey I couldn't stand it.
Literal
Next [at-に] sat man [of-の] person [subject-が] whiskey [of-の] smell [object-を] strongly causing, could-not-endure.
プンプン is a mimetic (擬態語) for a strong smell wafting intensely. ~を立てる here means 'to give off, emit.' がまん ('endurance, patience') + できない ('cannot') = 'could not endure.' A vivid complaint.