Four unique even numbers are arranged in ascending order and the first two are decreased by 50%, while the last two are increased by 50%. If the original sum of the 4 numbers was 162, the new sum can be? In the solution it is mentioned that the last two numbers must be 4 greater than the first two. Why?

When arranged in ascending order, the difference between 2nd term and 3rd term must be at least 2. Now when 2nd number is reduced by 50% and 3rd term is increased by 50% , so the difference between them will increase by 2. Thus the minimum difference would be 4. Hope it clears your doubt.
Since the question says can be, options are needed to tell the answer.