In a grid of 2 rows and 3 columns, one long diagonal is drawn across each row so that the two meet at the right end. How many triangles are there in the figure?

In each row the diagonal makes 3 triangles with the line above it and 3 with the line below it: $2\times 6=12$. The two diagonals also meet at the right end and form 3 triangles with the full-height uprights (the left edge and the two inner uprights). Total $12+3=15$.