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Explanation:

∣x2 − x − 6∣ = x + 2

∴ ∣(x − 3)(x + 2)∣ = x + 2 

Case 1: x < −2. i.e. (x − 3)(x + 2) > 0

(x - 3)(x + 2) = x + 2  

∴ x = 4. (which is rejected since  4 is not less than −2)

Case 2: x = −2.

This is a real root of this equation.

Case 3: −2 < x < 3. i.e. (x − 3)(x + 2) < 0

- (x - 3)(x + 2) = x + 2  

∴ x = 2.

Case 4: x = 3.

This does not satisfy the equation so x = 3 is not a root of this equation. 

Case 5: x > 3. (x − 3)(x + 2) > 0

(x − 3)(x + 2) = x + 2 

∴ x = 4.

Required product = (−2) × 2 × 4 = −16.

Hence, option (a).

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