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If $- 4 \leq x < 2$ then $| | x + 2 | - 3 |$ liesintheinterval

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Correct option is C

We have −4≤x<2⇒ −2≤x+2<4⇒ 0≤|x+2|<4⇒ −3≤|x+2|−3<1⇒ 0≤∥x+2|−3|≤3

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If −4≤x<2 then ||x+2|−3| liesintheinterval

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If $- 4 \leq x < 2$ then $| | x + 2 | - 3 |$ liesintheinterval