In double table tennis does rules allow to serve in to table side (red line) or only in to green ?
Player B is serving.
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Rule 2.6.3 of the official rules states:
in doubles, the ball shall touch successively the right half court of server and receiver.
There is no requirement that the ball crosses the end line of the receiving team - but note that the serve you've drawn would result in the server losing the point as it is not touching the right half court of the server and the receiver.