Two identical twins can only be distinguished by the characteristic that one always tells the truth and the other always lies. one twin tells you of a lucky number pair: "when i multiply my first lucky number by 3 and my second lucky number by 6, the addition of the resulting numbers produce a sum of 12. when i add my first lucky number and twice my second lucky number, the sum is 5." which twin is talking? how do you know?

To get a sum of 12, you know that the lucky numbers must be pretty small.  The first lucky number is 2, multiplied by 3 gets us 6.  The second lucky number is 1, multiplied by 6 gets us 6.  6 + 6 = 12.
The solve the next problem, the second lucky number (1) twice is 2.  When added to the first lucky number, the sum is 4.  This is tricky, because if the first lucky number was multiplied by 2 and added to the second lucky number, the sum would be 5.
In this case, the twin that lies is talking.