If a parallelogram is cut by two sets of m lines parallel to its...

The two sets of $m$ parallel lines along with two sets of two parallel lines of the given parallelogram will form two sets of $\left(m + 2\right)$ parallel lines. Each parallelogram is formed by choosing two parallel lines from each of the above

$∴$ Total number of parallelograms

$= C2 m + 2 \times C2 m + 2 = \left(C2 m + 2\right)2$

Hence, option (c) is correct.