Question
$$x+4 = x-12$$
Answer
This equation has no solution.
Explanation
$$ \begin{aligned} x+4 &= x-12&& \text{move the $ \color{blue}{ x } $ to the left side and $ \color{blue}{ 4 }$ to the right} \\[1 em]x-x &= -12-4&& \text{simplify left and right hand side} \\[1 em]x-x &= -16&& \\[1 em]0 &= -16&& \\[1 em] \end{aligned} $$
Since the statement $ \color{red}{ 0 = -16 } $ is FALSE, we conclude that the equation has no solution.
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