Answer
$9m^2-6my+y^2-z^2$
Work Step by Step
Using $(a+b)(a-b)=a^2-b^2$ or the product of the sum and difference of like terms, the given expression, $
[(3m-y)+z][(3m-y)-z]
,$ is equivalent to
\begin{array}{l}\require{cancel}
(3m-y)^2-(z)^2
\\\\=
(3m-y)^2-z^2
.\end{array}
Using $(a+b)^2=a^2+2ab+b^2$ or the square of a binomial, the expression above is equivalent to
\begin{array}{l}\require{cancel}
[(3m)^2+2(3m)(-y)+(-y)^2]-z^2
\\\\=
9m^2-6my+y^2-z^2
.\end{array}