After labelling the figure, we get the following,

• Simplest triangles AGE, EGC, GFC, BGF, DGB and ADG (6)
• Triangles with two components each AGC, BGC, and ABG (3)
• Triangles with three components each AFC, BEC, BDC, ABF, ABE and DAC (6)
• Triangles with six components is ABC (1)

Total number of triangles in the figure is 6 + 3 + 6 + 1 = 16

Hence option A is correct.