Solving proportions with $3$ ratios,$ x:3:y = -2:3:-4$

Just like chained equalities, you can break it apart. $x:3:y=-2:3:-4$ becomes $x:3=-2:3$ and $3:y=3:-4$. Now solve them independently.

We have: $x:3:y=-2:3:-4$

$\Rightarrow x:3=-2:3$

$\Rightarrow \dfrac{x}{3}=-\dfrac{2}{3}$

$\Rightarrow x=-2$

and

$\Rightarrow 3:y=3:-4$

$\Rightarrow \dfrac{3}{y}=-\dfrac{3}{4}$

$\Rightarrow \dfrac{y}{3}=-\dfrac{4}{3}$

$\Rightarrow y=-4$

$\therefore x=-2,y=-4$