Ditto on the above--and also search these forums as the 3203 is a common kart (i have 1) that many of us have fixed and modified and posted the pics and info here. (there's enough info in fact that us lowly yerf owners should have our own sub forum wink wink at BM .))))
Below is a link to a page that will give you an automatic download of a tecumseh factory carb ID and rebuild manual that includes a jet chart/part number listing. the carb you have is most likely a series 8. If you scroll down, the one you want is dated sept 2 2010 at 8:50 Click on that and once the download completes, open up "my documents" and go into the "downloads" folder to open it. There are a full tec series of factory manuals on that page for other aspects of servicing and rebuilding.
http://www.barrettsmallengine.com/manual/
FWIW, Tecs get a bad rap that I'm in the tiny minority who feels it's unwarranted. While there aren't any real hi-po parts for this engine, its service life if treated decently, is pretty robust. As far as carb parts go, most of the primary gaskets interchange between the various different series. A rebuild kit should run you about 10-20 bucks shipped. The intake pipe between the carb and head can be ported with a dremel or grinding stone in a drill, tube headers are easy to fabricate and cheap to buy, as is a new carb intake air filter plate. Along with that, toss in a $4-6 adjustable needle assembly to replace the fixed jet/bowl screw and you've got a nicely hopped up Tec for all of 10 to 30 bucks. There are a couple guys who a few years back also did various "stage" performance kits including valve springs, cams etc, don't know if they're still around. if you want to go that route--more pricey ---search "Batman modifications" on the web and you'll find his site and contact info.
or you could plunk down a Ben Franklin or more and bolt on a new clone mill ...