The lines intersect at 12 points
Therefore x * y = 12
Since x > y possibilities are x = 6 and y = 2 or x = 4 and y = 3
We need 4 points to form a paralleogram, 2 points forming 1 line and the other 2 points forming the other line.
When x = 6 and y = 2, the number of parallelograms formed = ^{6}C_{2} × ^{2}C_{2}
= 15 x 1 = 15
When x = 4 and y = 3, the number of parallelograms formed = ^{4}C_{2} × ^{3}C_{2}
= 6 x 3 = 18
Maximum = 18
Correct Answer: (C). 18 paralleograms