‘And they delivered the king's commissions to the king's satraps, and to the governors of Beyond the River, and they furthered the people and the house of God.'
The community leaders (they), then ensured the delivering of the king's commissions, as contained in his decrees, to the Persian authorities, that is to the king's satraps and to the governors of the administrative districts in Beyond the River. The plural satraps may suggest that there was at this time a satrap over Beyond the River as well as an overall satrap over the satrapy of Babylon (which initially at least included the province of Beyond the River), and that both made themselves available in order to receive the king's commissions, possibly having been advised about them beforehand by the king. In view of the importance of a decree from the king both may well have seen it as necessary to be present at the negotiations with Israel's representatives as they worked out together how they should be fulfilled. Alternately one of them might have been a visiting satrap from another satrapy who took part in the official ceremony, even possibly as a twofold witness (we can compare how, in Acts, when King Agrippa was visiting Festus he took part in the trial of Paul - Acts 25). But the two are mentioned because that is the number of satraps that Israel's representatives saw, not necessarily because there were two official satraps of Beyond the River.
‘And they furthered the people and the house of God.' This may refer to the satraps, and the governors of administrative districts within the satrapy, in that they expeditiously fulfilled the requirements of the decree. Or it may refer to the leading men of Israel as they carried out their part in the fulfilling of the decree. Indeed it may refer to both. Whichever way it is the point being made is that the Persian rulers did what was right by God's people, in enhancing the Temple, and ensuring that it fully fulfilled its purpose in encouraging the worship of God, whilst the leaders of Israel played their part in ensuring the same.