The image is a bit hard to make out, so I'm going to make some guesses. It looks like it says [tex]PN=12[/tex], [tex]QP=8[/tex], and [tex]PM=17[/tex], and you're asked to find [tex]QR[/tex].
You know that [tex]\Delta NPM[/tex] and [tex]\Delta NQR[/tex] are similar, which means their corresponding sides are proportional in length. So there's some constant [tex]c[/tex] such that
[tex]NP=cNQ[/tex]
[tex]PM=cQR[/tex]
[tex]MN=cRN[/tex]
To find [tex]QR[/tex], you need to know [tex]PM[/tex] and the constant [tex]c[/tex].
Clearly, [tex]NQ=NP+PQ=12+8=20[/tex]. So, the first equation becomes
[tex]NP=cNQ\iff12=20c\implies c=\dfrac{12}{20}=\dfrac35[/tex]
Then in the second equation, you have
[tex]17=\dfrac35QR\implies QR=17\times\dfrac53=\dfrac{85}3=28.\overline3[/tex]
