Krark’s Other Thumb works with any die you’re instructed or allowed to roll.

The ignored roll never happened as far as any other effect is concerned. For example, an ability that triggers “whenever you roll a die” won’t trigger for the ignored roll.

If you are instructed to roll multiple dice, roll two for each one and choose which one counts.

If the die roll includes a physical component, such as Ol’ Buzzbark caring where the dice land, roll two dice for each one you would roll. You may need to use colored dice to keep each pair of dice clear so you can ignore one roll from each pair.

Krark’s Other Thumb applies to rerolls as well.