After labelling the figure, we get the following,

• Simplest triangles APQ, AEQ, QTU, QRU, BGS, BHS, RSU, SUV, TUW, UWX, NWD, WDM, UVY, UXY, JCY and YKC (16)
• Triangles with two components each QUW, QSU, SYU and UWY (4)
• Triangles with three components each AOU, AFU, FBU, BIU, UIC, ULD and OUD (8)
• Triangles with four components each OYW, QSW, QSY and SYW (4)
• Triangles with six components each AUD, ABU, BUC and DUC (4)
• Triangles with seven components each QMC, ANY, EBW, PSD, CQH, AGY, DSK, and BJW (8)
• Triangles with twelve components each ABD, ABC, BCD and ACD (4)

Total number of triangles in the figure is 16 + 4 + 8 + 4 + 4 + 8 + 4 = 48

Hence option D is correct.