What is the number of triangles that can be formed whose vertices are the vertices of an octagon but have only one side common with that of octagon?

As per the given above question figures , we can see that
In each subsequent figure the design rotates through 90° clockwise and the oblique lines are rearranged.
Therefore , figure ( 2 ) will come on the place of ? in question figure .As shown in answer figures .

The element moves in the sequence.

On the basis of question figure pattern ,
Here the common faces with star are in same positions .
When the heart shape is at the top, the rhombus would be on the bottom.

As we can see that The fourth figure is different from the other three figures.So , figure ( 4 ) is correct answer .

On the basis of given figures in above question , we can see that
From first figure to third figure two smaller line segments are added. Similarly, two smaller line segments should be added to the second figure to get the Answer figure.
Hence , figure ( 2 ) will come on the place of ? in question figure .As shown in answer figures .

Since cutting from the mid line , it will create a circle around the mid line.