How Many Triangles?

The way this problem is set up, the intersections of purple and pink line segments form the third vertex of each triangle. Four purple line segments and three pink ones implies:

$\boxed{4 \times 3 = 12}$

Wouldn't it be 13..the whole thing is a triangle with the black line being a base

Every triangle to be counted must have the black side, one purple side and one pink side. Combinatorics says there are four purple sides and three pink ones. So there are 4 choices for the purple side and three for the pink side, and 4*3 = 12. To check, you can count the points of intersection between the pink and purple lines (the possible top vertices of the triangles). The bottom purple line intersects exactly once with each pink line, and those points of intersection define three triangles. The second purple line also intersects exactly once with each pink line, as do the third and fourth purple lines. 3 + 3 + 3 + 3 = 12.

There are many more than 12 triangles in the image, but only 12 of them have the black line as a side.