To construct parallelogram ABCD with the given data, follow the steps below:

1. Draw a line segment AB of length 4 cm. This will be one side of the parallelogram.
2. From point B, draw a line segment BC of length 3.2 cm in the direction opposite to point A. This will be another side of the parallelogram.
3. To construct point C, draw a circle with center A and radius 6.2 cm. This circle intersects the line segment BC at two points. Choose the point that is in the opposite direction of point B. Label this point as C.
4. Join points A and C. This line segment will be the diagonal of the parallelogram.
5. Draw a line perpendicular to line segment AB at point A. This line should intersect the line segment AC at point D.
6. Label point D as the intersection of the perpendicular line and line segment AC.
7. Join points B and D. This line segment will be the other diagonal of the parallelogram.
8. Check if the opposite sides of the parallelogram are parallel by measuring the angles between the diagonals. If the angles are equal, the sides are parallel.

A /—–——/ B
D/——––/ C

here, AB = 4cm (side)
BC = 3.2cm (side)
AC= 6.2cm (diagonal)
BC=AD=3.2cm (opposite sides of parallelogram are equal)
CD=AB=4cm (opposite sides of parallelogram are equal)
Steps :
Firstly take diagonal AC of 6.2cm as base.
Now from point A cut an arc of 4cm using compass upside.
With C as centre, cut another arc of 3.2cm upside.
Name the intersecting point as B.
Join AB and BC.
With A again as center, cut an arc of 3.2cm downward.
With C as centre, cut another arc of 4cm downside.
Name the intersecting point as D.
Join AD and CD
Thus Parallelogram ABCD is constructed!

Thankyou!