AC being parallel to RP makes the triangles ABC and RBP similar. This means corresponding sides occur in the same ratio, so that
[tex]\dfrac{AC}{RP}=\dfrac{BC}{BP}=\dfrac{AB}{RB}[/tex]
It's not clear from the picture what it is that you're supposed to find, but from the above relation we have
[tex]\dfrac{18}{RP}=\dfrac{BP+10}{BP}=\dfrac{14+7}7[/tex]
From this it follows that
[tex]\dfrac{18}{RP}=\dfrac{21}7=3\implies RP=\dfrac{18}3=6[/tex]
and
[tex]\dfrac{BP+10}{BP}=\dfrac{21}7=3\implies BP+10=3BP\implies2BP=10\implies BP=5[/tex]
