\(\dfrac{y}{2}+\dfrac{y+y}{3}+\dfrac{y+y+y}{4}=\dfrac{13}{12}\)
\(\dfrac{1}{2}y+\dfrac{2}{3}y+\dfrac{3}{4}y=\dfrac{13}{12}\)
\(y\left(\dfrac{1}{2}+\dfrac{2}{3}+\dfrac{3}{4}\right)=\dfrac{13}{12}\)
\(\dfrac{23}{12}y=\dfrac{13}{12}\)
\(y=\dfrac{13}{12}\div\dfrac{23}{12}=\dfrac{13}{23}\)