If a seven digit number made up of all distinct digits $8,7,6,4,3,2,xandy$ is divisible by 3, then

Seven digits are $8,7,6,4,3,xandy$

Sum of digits is $8+7+6+4+3+x+y$

$=28+x+y$

Maximum value of $x-y$is $9$, then $x$ is $9$ ,$y=0$

$28+9+0=37$ is not divisible by $\text{'}3\text{'}$

Maximum value of $x+y$ is $12$, then $28+12=40$is not divisible by $\text{'}3\text{'}$

Minimum value of $xy$ is $0$ then $x=2,y=0$

$xy=20,x+y=2$,$28+2=30$ is x is visible by $\text{'}3\text{'}$