#### Answer

$y=0$ or $y=3$

#### Work Step by Step

$4|2y-3|-1=11\longrightarrow$ add 1 to each side
$4|2y-3|-1+1=11+1\longrightarrow$ add
$4|2y-3|=12\longrightarrow$ divide each side by 4
$4|2y-3|\div4=12\div4\longrightarrow$ divide
$|2y-3|=3\longrightarrow$ definition of absolute value
$2y-3=-3$ or $2y-3=3$ solve each equation
$2y-3=-3\longrightarrow$ add 3 to each side
$2y-3+3=-3+3\longrightarrow$ add
$2y=0\longrightarrow$ divide each side by 2
$2y\div2=0\div2\longrightarrow$ divide
$y=0$
OR
$2y-3=3\longrightarrow$ add 3 to each side
$2y-3+3=3+3\longrightarrow$ add
$2y=6\longrightarrow$ divide each side by 2
$2y\div2=6\div2\longrightarrow$ divide
$y=3$