Solving Modulus Inequalities: When to use and not use distributive property

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I'm going to use examples to explain what I mean.

Solve $|d| + 6 \leq 10$.

\begin{align} |d| + 6 \leq 10 \implies d + 6 \leq 10 \implies d \leq 4 \end{align} or \begin{align} -d-6 \leq 10 \implies -d \leq 16 \end{align} So, $d \leq 4$ or $d \leq -16$

is incorrect. Why? It seems to make sense to me. The only difference I can see between this and other questions I got correct is that I distributed the negative sign first (or, earlier compared to the rest.)