Answer
$\displaystyle \frac{y+4}{y-4}$
Work Step by Step
When one denominator is the opposite, or additive inverse of the other,
first multiply either rational expression by $\displaystyle \frac{-1}{-1}$
to obtain a common denominator.
$\displaystyle \frac{y}{y-4}-\frac{4}{4-y}\cdot \displaystyle \frac{-1}{-1}$ $= \displaystyle \frac{y}{y-4}-\frac{-4}{-(4-y)}$
$= \displaystyle \frac{y}{y-4}-\frac{-4}{y-4} \qquad ... -\displaystyle \frac{-A}{B}=+\frac{A}{B}$
$= \displaystyle \frac{y}{y-4}+\frac{4}{y-4}$
... To add/subtract rational expressions with the same denominator,
add/subtract numerators and place the sum/difference over the common denominator.
= $\displaystyle \frac{y+4}{y-4}$