After labelling the figure, we get the following,

1. Simplest triangles ABF, BIC, CIH, GIH, FGE and AFE (6)
2. Triangles with two components each ABE, AGE, BHF, BCH, CGH and BIE (6)
3. Triangles with three components each ABH, BCE and CDE (3)

Total number of triangles in the figure is 6 + 6 + 3 = 15

Hence option D is correct.