Always look for common monimial factors over the terms of the polynomial. In this case, 2 is a common factor. Now, we have
You should recognize the difference of two squares. You should memorize the pattern for factoring it. I'll leave the finish for you.
You may or may not recognize this as a perfect square trinomial, but you should see that the first and last terms are perfect squares. You should also memorize a factorization pattern for this.
You can do the rest.
You should notice that the two middle terms are like terms and can be combined (even though the variables are in a different order).
Now, find your monomial factor of 6z and factor it out.
See if you can finish factoring the trinomial.