To be drinkingtwo beers (bottles) at once. Makes for a clankin' sound when ur drunk enough or just can't handle holding two bottles. Also known as "double fisting."
Mostly, clankin' tankards just means getting sloshed - most likely in a medieval setting. However, the phrase could absolutely be a euphemism for something (like getting railed in a sundress by an Hobgoblin, or getting boofed by a Bugbear).
"Avast ye! Hast thou been Clankin' Tankards at the Gasping Gander?? I can see the juicesall overyer face!"
With the balls actually having nothing to do with it, but initially thought by others to have been the use of the balls to produce the magical sound ball clankin creates. It is an action where your slap your dick against your stomache, preferably when it's wet out of the shower, to get the nice clankin noise that it produces to piss off your roommates early in the morning.