Spoiler for I got it!!!

1982 *|* 2010 = 16

1982 *|* 2010 = 16

Spoiler for solution

The aliens had the numbering system with the base 3, so they only had digits 0, 1 and 2. Operation *|* is performed on each corresponding digit of a number in the following manner - if the 2 digits are the same then the result is the same (e.g. 0 *|* 0 = 0, 1 *|* 1 = 1, 2 *|* 2 = 2). If the digits are different, the the result is the 3rd remaining digit (e.g. 0 *|* 1 = 2, 1 *|* 2 = 0, 0 *|* 2 = 1). To compute the result for any 2 numbers first convert the numbers to base 3 representation and then apply the operation digit-by-digit. For example,

The aliens had the numbering system with the base 3, so they only had digits 0, 1 and 2. Operation *|* is performed on each corresponding digit of a number in the following manner - if the 2 digits are the same then the result is the same (e.g. 0 *|* 0 = 0, 1 *|* 1 = 1, 2 *|* 2 = 2). If the digits are different, the the result is the 3rd remaining digit (e.g. 0 *|* 1 = 2, 1 *|* 2 = 0, 0 *|* 2 = 1). To compute the result for any 2 numbers first convert the numbers to base 3 representation and then apply the operation digit-by-digit. For example,

012001 *|* 012122 ------ 012210