4. Let the function $y=f(x)$ satisfy for all real numbers $x$
$$
f(3+x)=f(3-x),
$$

and the equation $f(x)=0$ has exactly 6 distinct real roots, then the sum of these 6 roots is
(A) 18 ;
(B) 12 ;
(C) 9 ;
(D). 0 .
4. (A)

If $3+\alpha$ is a root of $f(x)=0$, then by the given information
$$
f(3-\alpha)=f(3+\alpha)=0,
$$
$$
3 \pm \alpha_{1}, 3 \pm \alpha_{2}, 3 \pm \alpha_{3}
$$

Thus, their sum equals 18.