$$ -\frac{1}{4}\sqrt{32} = -\sqrt{\left(\frac{1}{4}\right)^2} \cdot \sqrt{32} = -\sqrt{\frac{1}{16}} \cdot \sqrt{32} = -\sqrt{\frac{1}{16} \cdot 32} = -\sqrt{2} $$
Ответ: $$ -\sqrt{2} $$