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.
In this case, the first two sides measure 4 and 6.
To determine if the third side can be 1, we would need to check if 4 + 1 > 6 and 6 + 1 > 4. Both of these conditions are met, so 1 could be the third side of the triangle.
To determine if the third side can be 2, we would need to check if 4 + 2 > 6 and 6 + 2 > 4. Both of these conditions are met, so 2 could be the third side of the triangle.
To determine if the third side can be 9, we would need to check if 4 + 9 > 6 and 6 + 9 > 4. Only the first condition is met but not the second, so 9 cannot be the third side of the triangle.
To determine if the third side can be 11, we would need to check if 4 + 11 > 6 and 6 + 11 > 4. Neither of these conditions are met, so 11 cannot be the third side of the triangle.
Therefore, the correct option is either 1 or 2.