Answer
$(-6,0)$
Work Step by Step
The solutions of $|u| \lt c $ are the numbers that satisfy $-c \lt u \lt c.$
The idea is to isolate $x$ in the middle.
Adding, subtracting or multiplying/dividing with a positive number preserves order (the inequality symbols remain).
Multiplying/dividing with a negative number inverts the order (the inequality symbols changes).
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$|\displaystyle \frac{2y+6}{3}| \lt 2\qquad $... is equivalent to ...
$-2 \lt \displaystyle \frac{2y+6}{3} \lt 2\qquad $ ... multiply all parts with $3$
$-6 \lt 2y+6 \lt 6\qquad $ ... add $-6$ to all parts
$-12 \lt 2y \lt 0 \qquad $ ... divide with $2$
$-6 \lt y \lt 0$
The interval borders are excluded from the interval.
The solution set is $(-6,0)$
