Three times the lesser of two consecutive even integers is 6 less than six times the greater number. find the integer

Let the lesser even integer be n.

Then 3n = 6(n+2)-6
          3n = 6n + 12 - 6
           -6 + 3n, and n = -2

The greater even integer is 0.

Check:  3(-2) = 6(0)-6
               -6    =   -6   true