Corresponding sides of the two triangles occur in a ratio with one another. In particular, you have the relationship
[tex]\dfrac6{6+x}=\dfrac{10}{15}=\dfrac y{y+4}[/tex]
We only need the first two parts to solve for [tex]x[/tex]:
[tex]\dfrac6{6+x}=\dfrac{10}{15}\implies6\cdot15=10(6+x)\implies90=60+10x\implies30=10x[/tex]
[tex]\implies\boxed{x=3}[/tex]
