Triangle Tiled Star

For easier to see, first I divide the six-sided star in to $6$ rhombuses along the blue lines here:

I noticed that the inner row of a rhombus has $2$ white triangles, the middle row has $6$ red triangles, the outer row has $10$ white triangles. It means the triangle increases $4$ on every row that has been added to a rhombus.

Therefore, the triangles needed to add to the $4^{th}$ layer is $10+4 = 14$ (triangles)

And, the star, as before, is created by 6 rhombuses, it means the total number of red triangles needed is $14 \times 6 = {\color{#D61F06}{\boxed{84}}}$ $\color{#D61F06}{red}$ triangles.

I split the star into 6 identical diamonds at each vertex then looked at an individual diamond. The pattern in each diamond goes: 2 grey, 6 red, 10 grey.. Term to term is +4. Therefore it would be 14 red triangles in the 4th layer of each diamond, 6 diamonds to consider; 14 x 6 is 84.

12, 36(=12+24), 60(= 36+24), 84(=60+24) (Ans.)

I split the star into 6 identical diamonds at each vertex then looked at an individual diamond. The pattern in each diamond goes: 2 grey, 6 red, 10 grey.. Term to term is +4. Therefore it would be 14 red triangles in the 4th layer of each diamond, 6 diamonds to consider; 14 x 6 is 84.