To solve this, we click to the page linked in the tweet, and scan it for links to the original report (or the original summary of the report). We find one such link:
A segment of the page with the phrase "report estimates that" highlighted. "Estimates" is linked.
That report seems to be the source of the claim, so we click through and find a summary of the finding from Adam Looney at the Brookings institution. And he has a link that shows his math.
A segment of the page with the phrase "how I arrived at this estimate" highlighted The phrase is linked.
The truth is we're not (most of us) risk researchers or even working economists. We're not going to be able to judge whether he is being fair about the math, whether he's citing consensus risk models or fringe stuff. We only have his reputation to go by.
It's a contentious issue, with a lot of complexity, so our goal here is not figuring out whether he is right. Our goal is to figure out how seriously to take that estimate. Is it junk, or is it worth considering? Do we keep reading, or do we go somewhere else?
So our second move, now that we know the original source, is to investigate the source.
In this case, a search for Brookings on Wikipedia shows that Brookings is a well respected think-tank that conducts this sort of policy analysis regularly, has a high marks for credibility, and seems to be centrist in political leanings, and not explicitly partisan.
The search above gave you a good result on Brookings — good enough for you to take the analysis seriously, in any case. Good enough for you to share this with others if that's what you want to do.
But I cannot stress enough that it doesn't mean you have to agree with the analysis. In fact, if you want to form an informed opinion on this question, you probably want to move to that (F) in SIFT, and find other trusted coverage on this issue of alcohol taxes and death rates. See what others say.
Students (and even teachers, sometimes) often want these things to resolve one way or another. Is this person right, or are they wrong? True or false? With some questions there's that sort of clarity, and we shouldn't hesitate to make simple judgments when simple judgments are merited.
For something like this, however, I like to think of it like food shopping. Maybe you're interested in this question of alcohol taxes. You go around the information supermarket, and you look at the (metaphorical) nutrition labels, and the question is not "Is this the only thing I will eat?" The question "Is this healthy enough to go in the shopping cart?"
The above analysis is healthy enough to go in the cart, and healthy enough to share with others. But if you have questions or concerns you should keep shopping! Just make sure that for the additional sources you consume you check those nutrition labels too.