The task is to find a test for divisibility by 6. Does it suffice to say that since 6=2*3, the test for divisibility by 6 must satisfy the tests for divisibility by both 2 and 3. So the resulting rule should be that for a number a in the form a=a_n***a_1 (where the notation means that each a_i is a digit, not that the a_i's should be multiplied) to be divisible by 6, 2 must divide a_1 and 3 must divide the sum of the digits of a [i.e. 3|a_n+. . .+a_1].
Sorry that I do not know how to use the special functions on the site to format the questions more neatly.