Distance between two parallel planes $2x+y+2z=8$  and $4x+2y+4z+5=0$ is

The planes are $2x+y+2z=8\to 1$

And $4x+2y+4z+5=0$  or $2x+y+2z+\frac{5}{2}=0\to 2$

$\therefore$ Distance between (1) and (2) $=\left|\frac{\frac{5}{2}+8}{\sqrt{2^2+1^2+2^2}}\right|=\left|\frac{21}{2\sqrt{9}}\right|=\frac{7}{2}$