Any carries that you did prior to March 29 did not count as the in game tracker was broken. It was fixed March 29 but was not made retroactive. Because of that, you are 2 carries short of the emblem as of right now. The in game tracker is all that matters, raid report means nothing for the emblem.
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The in game tracker is what the reward uses. You are, as others have stated, at 8 carries and need two more. Raid Report is not a Bungie affiliated application and, therefore, its statistics and counters can't be used as justification for triumphs and rewards.
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You're not listening. You had six carries when you did two more 2 days ago. Again...IT DOES NOT MATTER WHAT RAID REPORT SAYS OR SAID. Only the in game tracker matters. If you had looked at it 2 days ago, you would have seen 6.