Answer
$-\frac{1}{2}$
Work Step by Step
Given : $\frac{y-4}{10} \div \frac{4-y}{5}$
This becomes : $\frac{y-4}{10} \times \frac{5}{-(y-4)}$
$= \frac{y-4}{10} \times \frac{5}{-(y-4)}=-\frac{1}{2}$
(After dividing out the common factors $5$ $and$ $(y-4)$)