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
Given
$f(3+x)=f(3-x) \Rightarrow f(x)$ graph is symmetric about the line $x=3$, thus the 6 different real roots of $f(x)=0$ are also symmetric about the point $(3,0)$, with each pair summing to 6. Therefore, the sum of these 6 real roots is $3 \cdot 6=18$, so the answer is $A$.