The answer is 14 :
To find out the greatest sum of a number's possible factors you must choose those which are furthest from each other, in this case : [tex]6=6\cdot 1[/tex] 6 and 1 are the furthest. The length of long side of the rectangle is : 6 and the short side is 1. Lets calculate its perimeter : [tex]2(6+1)\\ 2\cdot 7=14[/tex]
The greatest possible perimeter is 14