Hi Amy, I'm not sure you'd really want to. The scales for all of these are completely out of whack. It's not clear what is being communicated. But having said that, it looks to be a dual axis chart with stacked bars on one axis, and standard bars on the other. So theoretically Tableau can do this. But an area chart might work better.
Post an excel file filled with dummy data and i am sure, a good Samaritan will design a nice viz for you.
In general I'm with Shawn that grouped stacked bars can be confusing, however this chart seems pretty straightforward. Assuming that your values are all elements of a dimension, the view is created using the following KB article: http://kb.tableausoftware.com/articles/knowledgebase/grouped-bar-chart. The one trick is that instead of using the dimension to set a value, we're using the dimension to set a date instead, I set this up in the attached.
If your data is coming through as a set of measures, to do this kind of view you're going to need to reshape your data so that the measures are members of a dimension. This is because Tableau does not give us access to the individual values of the convenience Measure Names/Values dimension/measure. I put together instructions for this and other variations at http://drawingwithnumbers.artisart.org/bars-and-lines/.
However, one thing that Tableau does not do is crosshatching. You might be able to pull something off with a dual axis and some transparency, but that would be a fair bit of extra work.
grouped bars.twbx.zip 1.1 MB