Marcus needs to rewrite f(x) = x2 + 6x + 4 in vertex form.

Set f(x) = y
 -> y = x^2 + 6x +4
Now, subtract 4 from both sides. 
 -> y - 4 = x^2 + 6x
Complete the square (take half of six and square it) and add this to both sides.
 -> y - 4 + 9 = x^2 + 6x + 9
Now we can rewrite x^2 + 6x + 9 with a perfect square.
 -> y + 5 = (x + 3)^2
Subtract 5.
 -> y = (x + 3)^2 - 5

Done.

Whose mistake? can you give more details to what the question is asking?