Well to start, vertex form is y=a(x-h)^2+k, where (h,k) is the vertex. a in this problem would be -1 because a is the constant before x^2. So, the sign on a tells you whether the quadratic opens up or opens down.
Your quadratic opens down. So to make this in vertex form you just plug it in.
y=(-1)(x-h)^2 +k
Now we have to figure out what h and k are.
h= -b/2a
h= -12/2(-1)
h= 6
So now your equation is y=(-1)(x-6)^2 +k
Now lets figure out what k is.
k= 4ac-b^2/4a
k=4(-1)(-4)-12^2
k=16+144
k=160/4(-1)
k=160/-4
k=-40
So your final equation is -1(x-6)^2-40
