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Yea, that's exactly how the explanation goes....ThanxThe key concept for this question is Newton's 3rd Law: for each force, there must be an opposing force with the same magnitude.
Since X and Y are connected together by the spring, when the spring is pulling X to give it acceleration, X is also pulling the spring (the opposing force). And this opposing force is transferred onto Y.
Thus, Y is experiencing a force with equal magnitude to the force on X.
And according to Newton's 2nd Law, since Y's mass is half of X, it should have an acceleration 2 times of X.