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Here in case of (1) it is more favorable towards SN1 reaction as it will create benzyl carbocation which is very stable.

(2) Here it is more favorable towards SN1 as it is first of all allyl carbocation and in resonance with the benzene and the double bond.

(3) It is allyl carbocation, so it is less favorable to SN1 than (1) and more favorable to SN2.

(4) It is the most favorable towards SN2 reaction.

Hence the order of reactivity towards SN2 reaction should be

(4) > (3) > (1) > (2)

But the answer is

(2) > (1) > (3) > (4)

Why?

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  • $\begingroup$ Are you sure the question is about $SN_2$ and not $SN_1$? Because your classification is correct with $SN_2$ $\endgroup$
    – Nicolas
    Feb 15 at 15:25
  • $\begingroup$ Yeah i am sure i can send the question picture if you want $\endgroup$ Feb 15 at 15:28
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The order you've given is absolutely correct with respect to SN2, I believe, the question needs to be authenticated once again, as the order for SN1 would be the exact reverse of this, which is as given in the answer to your question.

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