Considering the smaller and larger triangle, these two are similar triangles. Hence, 

If the height of the smaller triangle = h, 

\(\therefore \frac{h}{6} = \frac{h + 12}{12}\)

\(12h = 6h + 72 \implies 6h = 72\)

\(h = 12 cm\)

\(\therefore\) The height of the cone = 12 + 12 = 24 cm