6. (10 points) The large square grid shown is composed of 81 small squares, each 1 square centimeter in area, and $B, C$ are two grid points. If you are asked to mark another grid point $A$ such that the area of $\triangle A B C$ is exactly 3 square centimeters, then the number of such $A$ points is ( ).
A. 6
B. 5
C. 8
D. 10
【Analysis】According to the fact that the distance between two parallel lines is equal everywhere, it is only necessary to find a point on each side of $B C$ that meets the area of $3 \, \text{cm}^2$, and then draw parallel lines to find all the points.

【Solution】Solution: As shown in the figure, find points $A$ and $D$ on both sides of $B C$ such that the areas of $\triangle A B C$ and $\triangle B C D$ are both 3. Then draw parallel lines to $B C$ through points $A$ and $D$.

There are 8 grid points that meet the conditions.
Therefore, the answer is: $C$.