The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Since the first two sides measure 6 and 2, we can determine the possible range for the third side.
1. The sum of the first two sides is 6 + 2 = 8. Therefore, the third side must be greater than 8 - the greatest side but less than 8.
2. The greatest possible length for the third side is 8 - 2 = 6.
3. The third side must also be greater than the difference of the lengths of the first two sides, 6 - 2 = 4.
So, the possible whole number measures of the third side, listed in ascending order, are 5 and 6.