Start by simplifying the expression.
Remember that when you multiply numbers with the same base,  you can add the exponents together.

$6\left(x^{^{\frac{2}3{}}}x^{-1}\right)\left(y^{\frac{1}{4}}y^{\frac{1}{2}}\right)$ 

$6\left(x^{\frac{2}{3}-1}\right)\left(y^{\frac{1}{4}+\frac{1}{2}}\right)$  

$6x^{-\frac{1}{3}}y^{\frac{3}{4}}$ 

Substitute the given values for $x$ and $y$ then simplify.
Fractional exponents represent a power and a root.
The root is determined by the denominator, and the power by the numerator.
For example, the exponent for $16$ means the $4$th root of $16$ raised to the $3$rd power.

$6\left(27^{-\frac{1}{3}}\right)\left(16^{\frac{3}{4}}\right)$ 

$6\left(\frac{1}{3}\right)(8)$  

$16$