How to solve | x + 2 | + 16 = 14 ?

To begin, take 16 away from either side of the equation.
${\displaystyle \left|x+2\right|+16-16=14-16}$
${\displaystyle \left|x+2\right|+0=-2}$
${\displaystyle \left|x+2\right|=-2}$
By definition of the absolute value function the result of the function will always be greater than or equal to ${\displaystyle 0}$. This means that there is no answer to this issue, or the solution set is empty - ${\displaystyle x=\{\varnothing \}}$