It these triangles are similar, then the sides of the triangles are in proportion:
[tex]\dfrac{y}{10}=\dfrac{y+4}{15}[/tex] cross multiply
[tex]15y=10(y+4)[/tex] use distributive property
[tex]15y=10y+40[/tex] subtract 10y from both sides
[tex]5y=40[/tex] divide both sides by 5
[tex]\boxed{y=8}[/tex]
[tex]\dfrac{x}{4}=\dfrac{6}{8}[/tex] cross multiply
[tex]8x=(4)(6)[/tex]
[tex]8x=24[/tex] divide both sides by 8
[tex]\boxed{x=3}[/tex]
