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 which option could be the third side of a triangle, we need to find a value that is greater than the difference between the lengths of the first two sides (6 - 4 = 2) but less than their sum (4 + 6 = 10).
From the given options, the values that satisfy this condition are 2 and 9.
Therefore, the possible choices for the third side of the triangle are 2 and 9.