Answer
$\pm2,1\pm\sqrt 3i, -1\pm\sqrt 3i$ each zero has a multiplicity of 1.
Work Step by Step
$P(x)=x^6-8^2=(x^3+8)(x^3-8)=(x+2)(x^2-2x+4)(x-2)(x^2+2x+4)$
6 zeros can be found as $\pm2,1\pm\sqrt 3i, -1\pm\sqrt 3i$ each zero has a multiplicity of 1.