no, it is 44
the diomond in the center does have 12 if you count the 8 indevidual triangles,
however when you counted that there is 8 triangles per inner square, you also counted the indevidual triangles.
that makes 8 small triangles that you counted twice.
wich would make that answer 40.
however you did not count the 4 other triangles.
these 4 each have 2 corners in the outer corner of the whole picture, and the third corner is the center.
adding those 4,
the answer is 44