Let the given number be 476 $x$$y$ 0.

Then $\left(4 + 7 + 6 + x + y + 0\right)$ = $\left(17 + x + y \right)$ must be divisible by 3.

And, $\left(0 + x + 7\right)$ - $\left( y + 6 + 4\right)$ = $\left( x - y -3\right)$ must be either 0 or 11.

$ x $ - $ y $ - 3 = 0   $\Rightarrow y $ = $ x $ - 3

17 + $x$ + $y$ = $\left(17 + x + x - 3\right)$ = 2$ x $ + 14

$\Rightarrow x $= 2 or $ x $ = 8.

$\therefore x $ = 8 and $ y $ = 5.