The best I can figure, I can make 13
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6 straight lines drawn inside of an octagon will divide the octagon into 8 triangles
1
Draw a line from the midpoint of each side of the triangle to opposite corner. All three lines should intersect at the center of the original triangle and six smaller triangles will be formed. There are likely other solutions, but this is the easiest one.
You can make 6
6-2 = 4 triangles