Reduction of SUBSET-SUM to SET-PARTITION
What you are doing here is adding a new element to your original set 'X'. The value for this new element is (s - 2t). Hence, X' now contains one extra element as compared to X.

The SET-PARTITION would "accept" if the provided set can be partitioned into two subsets with equal sum. We were already able to pick out a subset 'Y', from the set X, the sum of whose elements was 't'. If we include the extra element (s-2t) in this subset Y, the sum of its elements would now become ( t + s - 2*t ) = (s-t). This is also the sum of the elements which are remaining in the set (X - Y). Hence, X' can be divided into two subsets each of whose sum is (s-t).