A rectangle is divided into two rows and four columns of equal squares, and one long diagonal runs from its top-left to its bottom-right corner. How many triangles are there?

The diagonal with the top edge and each upright line it crosses (three inner lines and the right side): 4. The same with the bottom edge: 4. The diagonal crosses the middle flat line at the centre; with that line it makes 2 triangles on each side (one closed by an outer side, one by the nearest upright line): 4. Total $4+4+4=12$.