#### Answer

$DY = 12$

#### Work Step by Step

First of all, we want to find the scale factor for the polygons.
To find the scale factor of two similar polygons, we find the ratio of the measures of corresponding sides.
Let's use sides that we know the definite measures of. This means we will use the corresponding sides.
$TREZ = \frac{4}{6}$
Divide both the numerator and denominator by their greatest common factor, $2$:
$TREZ = \frac{2}{3}$
The scale factor is $\frac{2}{3}$ or $2:3$.
Now that we have the scale factor, we can set up a proportion using the scale factor and $PA$ and $DY$ because $PA ≅ DY$:
$\frac{PA}{DY} = \frac{2}{3}$
Let's plug in what we know:
$\frac{8}{DY} = \frac{2}{3}$
Cross multiply to get rid of the fractions:
$2(DY) = 24$
Divide both sides by $2$ to solve for $DY$:
$DY = 12$