$\Delta PQR \sim \Delta DEF$ for the correspondence $PQR \leftrightarrow DEF$. If $3 PQ = 2 DE$,$EF = 6$,and $PR = 8$,find $QR$ and $DF$.

(N/A) Given that $\Delta PQR \sim \Delta DEF$.
Since the triangles are similar,the ratios of their corresponding sides are equal:
$\frac{PQ}{DE} = \frac{QR}{EF} = \frac{PR}{DF}$.
From the given equation $3 PQ = 2 DE$,we get $\frac{PQ}{DE} = \frac{2}{3}$.
Now,using the ratio $\frac{PQ}{DE} = \frac{QR}{EF}$:
$\frac{2}{3} = \frac{QR}{6} \implies QR = \frac{2 \times 6}{3} = 4$.
Next,using the ratio $\frac{PQ}{DE} = \frac{PR}{DF}$:
$\frac{2}{3} = \frac{8}{DF} \implies DF = \frac{8 \times 3}{2} = 12$.
Thus,$QR = 4$ and $DF = 12$.