Mean $$ = {{4 + 5 + 6 + 6 + 7 + 8 + x + y} \over 8} = 6$$

$$\therefore$$ $$x + y = 12$$ ..... (i)

And variance

$$ = {{{2^2} + {1^2} + {0^2} + {0^2} + {1^2} + {2^2} + {{(x - 6)}^2} + {{(y - 6)}^2}} \over 8}$$

$$ = {9 \over 4}$$

$$\therefore$$ $${(x - 6)^2} + {(y - 6)^2} = 8$$ ..... (ii)

From (i) and (ii)

x = 4 and y = 8

$$\therefore$$ $${x^4} + {y^2} = 320$$