Hanken is a place under Lunde gard in Balestrand.The Balestrand bygdabook, Tenningen gard, mentions your Britha Eriksdtr. Hanken as the 1794 wife of husmann Antonus Knutson.
Britha is not mentioned under Hanken. The husmann on Hanken at that time was Frik Olson, born at Hanken in 1728 and married in 1750 to Synneva Paulsdtr. Øvredal/Orvedal in Vik. I know that Erik and Frik are two different names but they often do get confused with each other and the dates would be about right for them to be Britha's parents. I could not find any mention of her at the Orvedal gard.