All even digit numbers in $B=\left\{2,4,6,8\right\}$ fav : forming a $4$ digit nos with all digit is even and not divisible by $4$

$2222, 6666, 2266$, 

$\frac{4!}{2!2!}=6$ cases

$\left(2226\right), \left(2666\right)$

$\frac{4!}{3!}=4$ cases   $\frac{4!}{3!}=4$ cases

Total $=1+1+6+4+4=16$ cases

Total : forming a $4$-digit no. from $\left\{1,2,\dots ,9\right\}$ but not divisible by $4$

$\mathrm{C}-1$ all $4$ digit are add $=5^4=625$

$\mathrm{C}-2$ all $4$ digit are even $=16$

$\mathrm{C}-3$ one even and $3$ odd 

you can not take $2$ or $6$ as one of even digit

$\left(12,16,32,36,\dots \right)$ all are divisible by $4$

But you can take $4$ or $8$ as one of even digit ...........

${}^2\mathrm{C}_1\times {}^4\mathrm{C}_1\times 5^3=1000$

Take one even digit out of $4$ and $8$ select one place for $4$ and $8$out of $4$-places

Total $=1000+625+16=1641$

$P=\frac{\mathrm{fav}.}{ \mathrm{total}}=\frac{16}{1641}$