hard counting

I count 14 ....  anyone else?   (edited)

hmm I think a better approach to this problem is to use complementary counting.

There are $\dbinom{6}{3}=20$ ways to choose 3 points to make a triangle. However 2  of these ways are just straight lines, so $20-12=\boxed{18} \text{ triangles. }$

I'm not sure if this is right, so please let me know if it's correct or not! 

:)