4. Let the function $y=f(x)$ satisfy $f(3+x)=f(3-x)$ for all real numbers $x$, and the equation $f(x)=0$ has exactly 6 distinct real roots. Then the sum of these 6 real roots is
(A) 18
(B) 12
(C) 9
( D ) 0
4. 【Analysis and Solution】If $3+a$ is a root of $f(x)=0$, then by the given $f(3-a)=f(3+a)=0$,
i.e., $3-a$ is also a root. Therefore, we can assume that the six roots of the equation $f(x)=0$ are $3 \pm a_{1}, 3 \pm a_{2}, 3 \pm a_{3}$.
Thus, their sum equals 18.