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\left(yx^{3}-2z^{2}\right)\left(y^{2}x^{6}+2yz^{2}x^{3}+4z^{4}\right)
Rewrite x^{9}y^{3}-8z^{6} as \left(yx^{3}\right)^{3}-\left(2z^{2}\right)^{3}. The difference of cubes can be factored using the rule: a^{3}-b^{3}=\left(a-b\right)\left(a^{2}+ab+b^{2}\right).