#### Answer

$y=\frac{1}{2}$

#### Work Step by Step

$\frac{1}{3}+\frac{4y}{6}=\frac{2}{3}\longrightarrow$ convert all fractions to a common denominator
$\frac{1}{3}+\frac{4y\div2}{6\div2}=\frac{2}{3}\longrightarrow$ simplify
$\frac{1}{3}+\frac{2y}{3}=\frac{2}{3}\longrightarrow$ subtract $\frac{1}{3}$ from each side
$\frac{1}{3}+\frac{2y}{3}-\frac{1}{3}=\frac{2}{3}-\frac{1}{3}\longrightarrow$ subtract
$\frac{2y}{3}=\frac{1}{3}\longrightarrow$ multiply both sides by $\frac{3}{2}$
$\frac{2y}{3}\times\frac{3}{2}=\frac{1}{3}\times\frac{3}{2}\longrightarrow$ multiply
$y=\frac{3}{6}\longrightarrow$ reduce
$y=\frac{3\div3}{6\div3}\longrightarrow$ simplify
$y=\frac{1}{2}$
When we plug our solution back into the equation, we find that each side of the equation is equal, making our answer correct.