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.