In a square, the middle of the left side is joined to both right-hand corners and the middle of the right side to both left-hand corners. How many triangles can you count?

The four lines cross at two points on the centre line. Smallest: one at the top, one at the bottom and four along the sides, 6. Each line with the top or the bottom edge and half a side makes 4 more. The two lines from one midpoint with the opposite side make 2 big ones. Total $6+4+2=12$.