Answer :

To form a parallelogram we need 2 sets of 2 parallel lines intersecting the other 2 lines from the other set. So, first of all, we need to get 2 lines from the sets. From the first parallel set, 2 out of 4 lines can be selected in ^{4}C_{2} = 6 ways. From the second parallel set, 2 out of 3 lines can be selected in ^{3}C_{2} = 3 ways. So, the total number of parallelograms can be formed is = (6 X 3) = 18.

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