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How is this 50 meters/yards per hex measured ?

As one hex is supposed to be 50 meters/yards how does this relate to center of hex to center of the next hex??

In attached diagram which is the correct 50 unit value??

One hex equeals 50 metters from side to side. Center to side would be 25 metters.

Thank on that part. So in a row it is straight forward to measure.

But how is this measured in a vertical manner. here a hex overlaps. So in the diagram which is 50 meters, line A or line B?

Line B joins the center of one hex to the centre of another hex so in theory it should be 50 meters. Line A is just the vertical distance between a line drawn through the centers of the hexs in a row and a similar line in the next row.

If line B is 50m then line A is about 43m
If line A is 50m them line B is about 56m

I know this is not useful for many things but map work there is some level of the need for understanding this.

Yes

Hex grid measurements have always been made from center-hex to center-hex, regardless of orientation, since the early days of wargaming. Because the center-to-center measurement = the side-to-side measurement, some games have used that instead. But no hex-grid game that I've ever seen made measurements like in Line A above; while that is the 'real' measurement, games usually "fudge" the vertical hexgrid measurements in order to keep the 6-axis movement system. 

This fudge issue is all well and good for "the game":

ORIGINAL: FlashfyreSP

Hex grid measurements have always been made from center-hex to center-hex, regardless of orientation, since the early days of wargaming. Because the center-to-center measurement = the side-to-side measurement, some games have used that instead. But no hex-grid game that I've ever seen made measurements like in Line A above; while that is the 'real' measurement, games usually "fudge" the vertical hexgrid measurements in order to keep the 6-axis movement system. 

But when working from maps and building them, such fudging will skew the actual XY relationships. So you end up with a stilted map.
hence the need to get the real meanings of these distances.

From center to center no matter in any of the 6 directions it will be 50 meters or yards. It doesnt say it is 50 yards from the center of one hex to the center of a side on another hex. Use a ruler for that. The grid would optimally be placed on top of a premade map.

In game terms this isnt really possible, the map has to be made inside the hexgrid system. Thats just the limits of the game.