1. Transform the terms into powers:
$\displaystyle \sqrt[4]{32xy^4} - y \cdot \sqrt[4]{162 xy^4} = \left(2 \cdot 2^4 \cdot x \cdot y^4 \right)^{\frac14} - y \cdot \left(2 \cdot 3^4 \cdot x \right)^{\frac14}$
2. Factor out $\displaystyle (2x)^{\frac14}$ and collect like terms in the bracket.
3. You should come out with $\displaystyle -y(2x)^{\frac14}$