In addition to SBurris answer, which is the way you should try first, I can assure you from my experience that what you want is in fact doable with BIRT, and even in two different ways.
However, some of the minor aspects might be a bit quite tricky for beginners, e.g. the merged cells in the column header, the different background colours and border widths for the columns. So, these style aspects shouldn't matter at first, you can tackle them later.
The first, by far easiest and standard way to achieve this kind of report layout is a cross tab, as SBurris said.
The second option is - depending on the database backend - to use a "normal" Table report item in they layout and to "create the cross tab" with SQL.
This is more powerful IMHO as the BIRT Cross Tab report item, but also more complicated.
For examples, see here:
(you get the idea)
To use this with BIRT, you'll have to select the column title values in addition to the cell values.
You have to decide how many columns do/should fit on your page (if you're using PDF output).
You can use the maximum aggregate function in the visibility expression of the columns to hide empty columns.
If the number of logical columns exceeds the number of columns for a single page, you can extend the idea further by dividing the cross tab into several, each with at most N columns.
However, note that this approach will need an experienced BIRT developer...