To solve this problem, you actually don't need to know the cone formula! This is simply the Pythagorean Theorem.
Using the theorem, which is \(a^2+b^2=c^2\) , we can insert our variables into the equation. Since \(c^2\) is the hypotenuse of the triangle, 12 will be our \(c\).
\(h^2+6^2=12^2\)
\(h^2+36=144\)
\(144-36=h^2\)
\(h^2=108\)
\(h=\sqrt108=6\sqrt3\)
So, the height of the cone is \(6\sqrt3\) cm.
Hope this helps!
Doggo