(4) The number of real solutions to the equation $\left|x^{2}-3 x+2\right|+\left|x^{2}+2 x-3\right|=11$ is $(\quad)$.
(A) 0
(B) 1
(C) 2
(D) 4
(4) The original equation can be transformed into
$$
|x-1|(|x-2|+|x+3|)=11 .
$$

When $x \leqslant -3$, the equation transforms into $2 x^{2}-x-12=0$, both roots of which are greater than -3, so there is no solution in this case;

When $-3 < x \leqslant 2$, the equation transforms into $|x-1|(5)=11$, which simplifies to $|x-1|=\frac{11}{5}$. This gives $x-1=\frac{11}{5}$ or $x-1=-\frac{11}{5}$, leading to $x=\frac{16}{5}$ or $x=-\frac{6}{5}$. Only $x=-\frac{6}{5}$ satisfies the condition $-3 < x \leqslant 2$;

When $x > 2$, the equation transforms into $2 x^{2}-x-12=0$, one of whose roots $x=\frac{1+\sqrt{97}}{4}$ satisfies the condition.
In summary, there are 2 real solutions that satisfy the equation. Therefore, the answer is $\mathrm{C}$.