Answer
$(-11,5)$
See graph.
Work Step by Step
Step 1. Remove the absolute value sign to get $-2\lt \frac{x+3}{4}\lt 2 \Longrightarrow -8\lt x+3\lt 8 \Longrightarrow -11\lt x\lt 5$ or $(-11,5)$
Step 2. See graph.
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