The maximum printing area will be a square. Call the side length of the printing area a. The rectangular poster will have one side = a+16 and the other side = a+12 to allow for margins. (a+16)(a+12)=6912. Therefore:
a^2+28a+192-6912=0; a^2+28a-6720=0; a^2+28a+196=6720+196; (a+14)^2=sqrt(6916)=83.1625 approx.
a=83.1625-14=69.1625cm. Therefore the poster size is approximately 69.16+16=85.16cm by 69.16+12=81.16cm.
Check: 85.16*81.16=6912sq cm.