10. In a Cartesian coordinate system, given points $A(-1,2)$, $B(1,2)$, $C(-3,1)$, $D(3,1)$, $E(-2,-2)$, $F(2,-2)$, $G(-4,3)$, $H(4,3)$. Using these eight points as vertices to form triangles, and ensuring that no two vertices of the triangle are symmetric with respect to the $y$-axis. Then the number of such triangles is ( ) .
(A) 8
(B) 24
(C) 32
(D) 56
10. C.

These eight points consist of four pairs of points that are symmetric about the $y$-axis.
The vertices of the triangles that meet the condition cannot be symmetric about the $y$-axis, so the total number of such triangles that can be formed is
$$
\frac{8 \times 6 \times 4}{3 \times 2 \times 1}=32 \text{ (triangles). }
$$