Answer
$32y-8\sqrt{y}+4z\sqrt{y}-z$
Work Step by Step
Using $(a+b)(c+d)=ac+ad+bc+bd$ or the FOIL method, then,
\begin{array}{l}
\left( 8\sqrt{y}+z \right)\left( 4\sqrt{y}-1 \right)
\\=
(8\sqrt{y})(4\sqrt{y})+(8\sqrt{y})(-1)+(z)(4\sqrt{y})+(z)(-1)
\\=
32\sqrt{y^2}-8\sqrt{y}+4z\sqrt{y}-z
\\=
32y-8\sqrt{y}+4z\sqrt{y}-z
.\end{array}