$\text{a)}\left(x^8:x^4\cdot x\right):\left(x^3:x\right)=\left(x^{8-4}\cdot x\right):x^{3-1}=\left(x^4\cdot x\right):x^2=x^{4+1}:x^2=x^5:x^2=x^{5-2}=x^3$

$\text{b)}\left[\left(y^6\cdot y^3\right):\left(y^{15}:y^{12}\right)\right]:y^3=\left[y^{6+3}:y^{15-12}\right]:y^3=\left[y^9:y^3\right]:y^3=y^{9-3}:y^3=y^6:y^3=y^{6-3}=y^3$

$\text{c)}{a}^{10}:\left[\left(a^3\cdot a^5\right):a\right]=a^{10}:\left[a^{3+5}:a\right]=a^{10}:\left[a^8:a\right]=a^{10}:a^{8-1}=a^{10}:a^7=a^{10-7}=a^3$

$\text{d)}\left(d^8:d\right):\left(d^{15}:d^{10}\right)=d^{8-1}:d^{15-10}=d^7:d^5=d^{7-5}=d^2$

$\text{e)}{b}^2\cdot b\cdot a^2\cdot b^3\cdot a^6=a^{2+6}\cdot b^{2+1+3}=a^8{b}^6$

$\text{f)}{z}^3\cdot e\cdot z\cdot e^3\cdot z^2\cdot e^5=e^{1+3+5}{z}^{3+1+2}=e^9{z}^6$