For |x|<=y set up a double sided inequality -y <= x <= y. You can either handle one side at a time, or handle both sides. Solve using regular algebra, but if you multiply or divide by a - number then switch the inequality sign.
In this problem: -4 <= (2/3)x <= 4 (multiply all sides by 3):
-12 <= 2x <= 12 (divide all sides/parts by 2):
-6 <= x <= 6.
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