The number of arrangements of all letters of the word ‘ANALYTICAL’ in which the two L’s do not appear adjacently is 

Total number of arrangements $\frac{10!}{3!2!}$
The number of arrangements in which two 
L’s appear adjacently = $\frac{9!}{3!}$
$\therefore$Total number of arrangements
$=\frac{10!}{3!2!}-\frac{9!}{3!}$
$=\frac{9!}{3!}\times 4=6(8!)$