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Just multiply 1/6 to every exponent in the expression:

(8 a^{3}  b^{6})^ \frac{1}{6}

(2^3a^{3}  b^{6})^ \frac{1}{6}

2^{(3)\frac{1}{6}} a^{(3)\frac{1}{6} }  b^{(6)\frac{1}{6} }

2^ \frac{1}{2} a^{\frac{1}{2}} b^{1}

(2a)^ \frac{1}{2}  b= \boxed{b \sqrt{2a} }