$(xy’+z)’\cdot((xz)’+y')$
$$\begin{align*} (xy’+z)’\cdot ((xz)’+y’) &=(x'+yz’)\cdot (x’+z’+y’)\\ &=x’x’ + x’z’ + x’y’ + yz’x’ + yz’z’ + yz’y’\\ &=x’ + x’z’ + x’y’ + yz’x’ + yz’ + z’ \end{align*}$$
Can it be further simplified?
$(xy’+z)’\cdot((xz)’+y')$
$$\begin{align*} (xy’+z)’\cdot ((xz)’+y’) &=(x'+yz’)\cdot (x’+z’+y’)\\ &=x’x’ + x’z’ + x’y’ + yz’x’ + yz’z’ + yz’y’\\ &=x’ + x’z’ + x’y’ + yz’x’ + yz’ + z’ \end{align*}$$
Can it be further simplified?
$$\begin{align*} (xy’+z)’\cdot ((xz)’+y’) &= (xy')'z'((xz)'+y')\\ &= (x'+y)z'(x'+z'+y')\\ &= (x'z' + yz')(x'+z'+y')\\ &= (x'z' + yz')x' + (x'z'+yz')z' + (x'z'+yz')y'\\ &= x'x'z' + x'yz' + x'z'z' + yz'z' + x'y'z' + yy'z'\\ &= x'z' + x'yz' + x'z' + yz' + x'y'z' + 0\\ &= x'z'(1+y+y') + yz'\\ &= x'z' + yz'\\ &= (x'+y)z'. \end{align*}$$