Final answer:
The greatest possible side length for each square piece is 6 cm.
Step-by-step explanation:
The paper measures 6 cm by 12 cm. To find the greatest possible side length for each square piece, we need to find the greatest common divisor (GCD) of the two dimensions. The GCD of 6 and 12 is 6. Therefore, the greatest possible side length for each square piece is 6 cm.