Answer
Solutions are $2, \frac{-14}{5}$
Work Step by Step
$|\frac{5x+2}{2}| = |-6|$
Absolute value of a negative number is positive number. So,
$|\frac{5x+2}{2}| = 6$
This is equivalent to
$\frac{5x+2}{2} = 6$ or $\frac{5x+2}{2} = -6$
$5x+2 = 12$ or $5x+2 = -12$
$5x= 12-2$ or $5x = -12-2$
$5x= 10$ or $5x = -14$
$x = 2 $ or $x = \frac{-14}{5}$
Solutions are $2, \frac{-14}{5}$