To reflect the point \( C(4, 4) \) over the \( x \)-axis, you change the sign of the \( y \)-coordinate while keeping the \( x \)-coordinate the same.
So, the \( y \)-coordinate of point \( C(4, 4) \) becomes \( -4 \) after reflection.
Thus, the reflected point \( C' \) will be:
\[ C' = (4, -4) \]
So your answer is:
\( C' = (4, -4) \)