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Measuring implies using a measuring device of some kind. If you mean to construct a hexagon without a protractor or ruler, that's different. Constructions in geometry require only a compass and a straightedge (a ruler, but you ignore the numbers). A hexagon can be made of 6 equilateral triangles; choose any length for the side and construct them connected together, using only the compass to set the length and the straightedge to draw straight lines between points.
Constructions that are impossible using only a compass and straightedge include Trisecting an angle Squaring a circle Doubling a cube
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No, it is not possible to construct a cube of twice teh volume of a given cube using only a straightedge and a compass.