∠AOB, the straight line L∨OB and OA intersect at point C, and an arc is drawn by ruler gauge, where de intersects with OA at point D and with straight line L at point E, so that DE=2cm.

Strictly speaking, the ruler can't be used for drawing with scales, and the topic conditions don't give the size of any line segment or arc, so this topic can't follow the strict ruler drawing method. Only a compass can be used to measure the distance of 2 cm on the scale.

The conditions of this problem are not sufficient, so there are many results.

Draw an arc with a radius of 2cm with any point d on the OA straight line (the distance from the straight line L is less than 2cm) as the center, and intersect with the straight line L at point E, then the line segment DE is the required 2cm line segment.

Draw an arc with a radius of 2cm with any point E on the straight line L (the distance from the straight line OA is less than 2cm) as the center of the circle, and intersect with the straight line OA at D, then the line segment DE is also the required 2cm line segment.