By definition, a parallelogram is a quadrilateral with opposite sides parallel and equal.
A parallelogram has four properties that can help us to solve this problem.
1 - Opposite angles are equal.
2 - Opposite sides are equal and parallel.
3 - Diagonals bisect each other.
4 - Sum of any two adjacent angles is 180°
For the first quadrilateral, KLMN, we have that ∠M is congruent to ∠L, but ∠K is not necessarily congruent to ∠N, and since opposite angles in a paralellogram are equal, this quadrilateral is not necessarily a paralellogram.
For the second quadrilateral, GHJI, we have a quadrilateral with two pairs of equal opposite sides. If we cut this triangle from 1 vertice to the opposite vertice, we're going to divide this quadrilateral into two similar triangles(by the SSS postulate), therefore, ∠H = ∠I and ∠G = ∠J, and this means the sides are also parallel, thus, this quadrilateral IS a paralellogram.
For the third quadrilateral, ABDC, we have the same idea as the previous quadrilateral. We divided this quadrilateral into two similar triangles, therefore, ABDC IS a paralellogram.
For the last quadrilateral, VWYX, by the same idea we had for GHJI, we have this parallelogram divided into similar triangles(by the SAS postulate), therefore, the corresponding angles and parallel sides are equal and VWYX IS a parallelogram.